Terminology for the theory of machines and mechanisms

Terminology for the Theory of Machines and Mechanisms I. STRUCTURE OF MACHINES AND MECHANISMS

1.1 Components MECHANISM ELEMENT: Solid body or fluid component of a mechanism. LINK: 1. Mechanism element (component) carrying kinematic pairing elements. 2. Element of a linkage. INPUT LINK: Link to which mechanical energy (motion and force) is imparted from a prime mover to be transformed into motions and forces of the other links. OUTPUT LINK: Link from which required forces and motions are obtained. DRIVING LINK: Link that transfers mechanical energy to at least one other link directly connected to it. DRIVEN LINK: Link that receives mechanical energy from at least one other link directly connected with it. (Note: Driving and driven links may change their functions within one period of mechanism movement). INITIAL LINK: Link in respect of which the generalized coordinate is prescribed. FRAME: Mechanism element assumed to be stationary, a support or foundation. BAR: Binary link. CRANK: Rotating link which may perform a complete revolution about a fixed axis. ROCKER: Rotating link that performs an incomplete revolution about a fixed axis. COUPLER (FLOATING LINK): Link connecting other links neither of which is the frame. SLIDER: 1. Link that forms a prismatic pair with one link (the frame) and a revolute pair with another (moving) link. 2. Prismatic pair. SLIDING BLOCK: Compact element of a prismatic pair which slides along a guiding element (e.g. in a slot). GUIDE: Element of a prismatic pair that constrains the motion of a sliding block. CROSSHEAD: Component (guided by slide bars) between a piston and a connecting rod to transmit the component of the force in the connecting rod normal to the slide bars. CROSSHEAD GUIDE: Slide bars that guide a crosshead and transmit the component of the force in the connecting rod normal to the line of stroke to the frame. CONNECTING ROD: Coupler between a piston or a crosshead and crank shaft. CAM: Component with a curved profile or surface that imparts a displacement either by point or line contact to the cam follower. DISK CAM: Rotating cam in the shape of a disk whereby the position of the cam follower is determined by radial distances from the cam axis. FACE CAM: Rotating cam with a groove in a plane surface or a rib on a plane surface which is perpendicular to the cam axis.

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CYLINDRICAL CAM [BARREL CAM]: Rotating cylinder with a curved groove in its surface or a curved rib on its surface where contact is made with the follower. GLOBOIDAL CAM: Cam formed by a ridge or a groove on a globoid. SPHERICAL CAM: Rotating cam in the shape of a part of a hollow sphere the radial surface of which is designed to make contact with a follower. YOKE CAM: Constant-breadth radial cam designed to mesh with a yoke follower. CAM FOLLOWER: Component receiving motion directly from a cam. YOKE FOLLOWER: Cam follower with two surfaces fixed to one another which contact two sides of the same cam. FRAME FOLLOWER: Yoke follower with two parallel plane surfaces which contact a yoke cam at two opposite lines or points. CAMSHAFT: The shaft on which a cam or cams are fitted. GEAR: Wheel with teeth on its surface designed to mesh with the teeth of another gear or rack. CYLINDRICAL GEAR: Gear with teeth formed on a cylindrical surface. SPUR GEAR: Cylindrical gear with external teeth. ANNULUS: Cylindrical gear with internal teeth. GEAR SECTOR [SEGMENT]: Segment of a spur gear or annulus. BEVEL GEAR [CONICAL GEAR]: Gear with teeth formed on a conical surface. HYPOID GEAR: Spiral-bevel gear pair with offset between the gear axes. HELICAL GEAR: Gear with teeth wrapped helically on a cylindrical surface. HERRING-BONE GEAR (DOUBLE HELICAL GEAR): Gear comprising two integral helical gears, the helices of the gears being of opposite hand. WORM: Gear with one tooth or more wrapped helically on a cylinder or a globoid to mesh with a worm gear whose axis is perpendicular to that of the WOrlTI.

WORM GEAR: Gear with teeth formed on a cylindrical or globoidal surface. PLANET GEAR: Gear that rotates on an axle the axis of which is constrained to rotate about another axis. PINION: The smaller of a pair of meshing gear wheels. RACK: Segment of a cylindrical gear of infinite radius. IDLER: Gear intermediate between a driving and a driven gear, which affects the sense of direction of the latter but not the velocity ratio. FRICTION GEAR: Wheel that transmits a driving force to the surface of a second component by friction at the point or line of contact. BELT: Flexible element used for the transmission of motion and force between two pulleys. PULLEY: Wheel on which a belt is wrapped to create a flexible link with a second pulley.

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CHAIN: Belt consisting of a number of short rigid links hinged together to form a loop. SPROCKET WHEEL: Wheel with teeth (sprockets) round its rim designed to engage the links of a chain. DRIVE SHAFT: Shaft used to transmit torque. CARDAN SHAFT: Drive-shaft connecting two universal couplings. PIVOT: 1. A fixed axis about which revolute motion can take place. 2. Male element of a revolute joint. JOURNAL: The male element of a revolute or cylindrical joint. BEARING: Machine component that allows relative motion (rotation, translation) and transmission of force between adjacent components. PAWL (CLICK, DETENT): Component which is intermediate between two elements and which prevents relative motion between them in one direction. LATCH: Movable component which holds another component in place by entering a notch or a cavity, e.g. the locking device of a ratchet. RATCHET: Element which has a frictional or serrated surface to engage with a pawl. STOP: Component of a machine that makes intermittent contact with an other component to provide a limit to their relative motion. 1.2 S u b - a s s e m b l i e s SUB-ASSEMBLY: Identifiable set of components forming part of a machine. JOINT: The physical embodiment of a kinematic pair. KINEMATIC PAIR: Contacting elements of links permitting their constrained relative motion. PAIRING ELEMENT: Assembly of surfaces, lines, or points of a link through which it may contact some other link so constituting a kinematic pair. DEGREE OF FREEDOM (CONNECTIVITY) OF A KINEMATIC PAIR: The number of independent coordinates needed to describe the relative positions of pairing elements. CLOSURE OF A KINEMATIC PAIR: The process of constraining two rigid bodies to form a kinematic pair by either force (force closure), geometric shape (form closure), or flexible materials (material closure). FORCE-CLOSED PAIR (OPEN JOINT): Kinematic pair the elements of which are held in contact by means of external forces. FORM-CLOSED PAIR: Kinematic pair the elements of which are constrained to contact each other by means of particular geometric shapes. LOWER PAIR: Kinematic pair which is formed by surface contact of its elements. HIGHER PAIR: Kinematic pair which is formed by point or line contact of its elements. REVOLUTE PAIR (HINGE, ROTATING JOINT, T U R N I N G JOINT): Pair for which the degree of freedom is one and which allows iotary motion of one link relative to the other.

PRISMATIC PAIR (SLIDING JOINT): Pair for which the degree of freedom is one and which allows rectilinear translation of one link relative to another. HELICAL PAIR (SCREW PAIR): Pair for which the degree of freedom is one and which allows screw motion. CYLINDRICAL PAIR: Pair for which the degree of freedom is two and which allows a rotation about a particular axis together with an independent translation in the direction of this axis. SPHERICAL PAIR: Pair for which the degree of freedom is three and which allows independent rotations about three separate concurrent axes. PLANAR CONTACT PAIR (SANDWICH PAIR): Pair for which the degree of freedom is three and which allows relative motion in parallel planes. CAM PAIR: Kinematic pair consisting of a cam and a follower in direct contact. UNIVERSAL JOINT (UNIVERSAL COUPLING, CARDAN JOINT, HOOKE'S JOINT): Kinematic joint connecting two shafts with intersecting axes. PIN JOINT: A joint using a pin as the interlocking component between two rigid bodies; used in linkages as a revolute pair. G E A R I N G (TOOTHED GEARING): Higher kinematic pair formed by successively contacting elements ("teeth") of two links. COUPLING: Device for joining two moving members, e.g. two shafts at their ends. CLUTCH: Coupling for torque transmission along a shaft that allows for easy engagement and disengagement during operation. FLYWHEEL: Rotor used for storing kinetic energy. ACTUATOR: Sub-assembly which causes motion of the parts to which it is attached in response to a signal. DRIVE: System of mutually connected devices for setting in motion one or several parts of a machine or a mechanism. BACKLASH (CLEARANCE): Difference between dimensions of mating parts that allows unconstrained motion. 1.3 M e c h a n i s m s MECHANISM: 1. System of bodies designed to convert motions of and forces on one or several bodies into constrained motions of and forces on other bodies. 2. Kinematic Chain with one of its components (link or joint) connected to the frame and with definite motion. STRUCTURE (OF MECHANISM): The number and kinds of elements in a mechanism (members and joints) and the sequence of their contact. STRUCTURAL ANALYSIS (OF MECHANISMS): Analysis of the structure of a mechanism. STRUCTURAL DIAGRAM: A simplified and schematic diagram of a mechanism emphasizing only its structure.

Terminology for the Theory of Machines and Mechanisms K I N E M A T I C D I A G R A M O F A MECHANISM: Diagram of a mechanism giving the dimensions of links necessary for kinematic analysis of the mechanism. ISOMORPHISM: The equality of structures in number of elements (members and joints), and the sequence of their contacts. EQUIVALENT MECHANISM: Mechanism whose kinematical properties are equivalent in some particulars to those of a mechanism having a different structure. C O G N A T E MECHANISM: Mechanism that is geometrically different from another but which, nevertheless, has the same transfer function. K I N E M A T I C CHAIN: Assemblage of links and joints. CLOSED K I N E M A T I C CHAIN: Kinematic chain each link of which is connected with at least two other links. OPEN K I N E M A T I C CHAIN: Kinematic chain in which there is at least one link which carries only one kinematic pairing element. K I N E M A T I C JOINT: Kinematic chain whose kinematical properties are equivalent in some particulars to those of a kinematic pair. LOOP: Subset of links that forms a closed circuit. TREE (MOBILE): Kinematic chain which contains no loops. D E G R E E O F F R E E D O M (MOBILITY) OF A K I N E M A T I C C H A I N OR M E C H A N I S M : Number of independent coordinates needed to define the configuration of a kinematic chain or mechanism. ASSUR GROUP: Kinematic chain which when added to, or subtracted from, a mechanism leaves the resulting mechanism with the same mobility as the original one, with the proviso that an ASSUR G R O U P may not encompass a smaller ASSUR GROUP. CONSTRAINT: Any condition that reduces the degree of freedom of a system. K I N E M A T I C INVERSION: The transformation of one mechanism to another by choosing a different member to be the frame. LIMIT POSITION OF A M E C H A N I S M : Configuration of a mechanism in which one of its links is in a limit position. LIMIT POSITION O F A LINK: Position of a link for which a coordinate which describes its position relative to an adjacent link is a maximum or a minimum. P L A N A R M E C H A N I S M : Mechanism in which all points of its links describe paths located in parallel planes. SPHERICAL MECHANISM: Mechanism in which all points of its links describe paths located on concentric spheres. SPATIAL M E C H A N I S M : Mechanism in which some points of some of its links describe nonplanar paths, or paths located in non-parallel planes. G U I D A N C E MECHANISM: Mechanism that guides a point of a link along a certain path or a

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member through a definite sequence of positions. FUNCTION-GENERATING MECHANISM (TRANSMISSION MECHANISM): Mechanism that generates a required functional relationship between the displacements of input and output link(s). P A T H - G E N E R A T I N G MECHANISM: Mechanism in which a point on a member generates a given path. STEP MECHANISM: Mechanism in which the output link performs unidirectional motion with periodic dwells. PILGRIM-STEP MECHANISM: Mechanism whose transfer function has the characteristic of an overall unidirectional motion but with periodically recurring reversals. DWELL MECHANISM: Mechanism in which the output link performs reciprocating or rocking motion with periodic dwells. D I F F E R E N T I A L MECHANISM: Mechanism for which the degree of freedom is two and which accepts two inputs to produce one output. S E L F - L O C K I N G MECHANISM: Mechanism transmitting motion and power in only one direction. ADJUSTABLE MECHANISM: Mechanism whose primary dimensions (e.g. link-lengths) can be altered. L I N K A G E (LINKWORK): Kinematic chain whose joints are equivalent to lower pairs only. F O U R - B A R L I N K A G E : Linkage with four binary links. F O U R - B A R MECHANISM: Mechanism with four binary links. C R A N K - A N D - R O C K E R MECHANISM: Fourbar mechanism with a crank and a rocker. D O U B L E - C R A N K M E C H A N I S M (DRAGL I N K MECHANISM): Four-bar mechanism with two cranks. P A R A L L E L - C R A N K MECHANISM: Four-bar mechanism having cranks of equal length and a coupler with length equal to that of the frame. DOUBLE-ROCKER MECHANISM: Four-bar mechanism with two rockers. SLIDER-CRANK MECHANISM: Four-bar mechanism with a crank and a slider. DOUBLE-SLIDER MECHANISM: Four-bar mechanism with two sliders. SCOTCH-YOKE MECHANISM: Four-bar mechanism in which a crank is connected by a slider with another bar, which in turn forms a prismatic pair with the frame. CAM MECHANISM: Mechanism including at least one cam. SCREW MECHANISM: Mechanism including at least one screw pair. W E D G E MECHANISM: Mechanism the links of which form prismatic pairs only. G E A R TRAIN: Assembly containing at least one pair of gears. P L A N E T A R Y G E A R T R A I N (PLANETARY TRAIN): Gear train containing at least one planet gear.

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MITRE GEAR: Bevel gear drive with equal gears whose axes intersect at right angles. P L A N E T - G E A R (EPICYCLIC-GEAR) MECHANISM: Mechanism consisting of planetary gear trains. BELT MECHANISM: Mechanism in which motion is transformed by means of a belt. C H A I N MECHANISM: Mechanism in which motion is transformed by means of a chain. G E A R E D LINKAGE: Combination of a linkage and a gear mechanism. GENEVA M E C H A N I S M (GENEVA DRIVE): Mechanism involving a crank whose pin intermittently engages a slot in the driven member (e.g. of Maltese-cross shape). 1.4 Machines MACHINE: Device performing mechanical motion to transform and transfer energy, material and information. ENGINE (PRIME MOVER): Machine designed to transform any other form of energy into mechanical energy. PUMP: Machine to create a directed liquid or gas flow. GENERATOR: Machine designed to transform mechanical energy into other forms of energy. PROCESS MACHINE: Machine which transforms materials by changing their position, shape, properties, dimensions and states. ROBOT: Machine for performing manipulative and locomotive functions able to interact with its surroundings with a certain degree of autonomy. I N D U S T R I A L ROBOT: Programmable handling unit. MANIPULATOR: Controlled technical system grasping, guiding and handling objects. W A L K I N G MACHINE: Controlled technical system for performing functions similar to locomotion of animals and men. PEDIPULATOR: Mobile supporting device (leg) of walking machine. 2. KINEMATICS

2.1 General KINEMATICS: Branch of theoretical mechanics dealing with the geometry of motion, irrespective of the causes producing the motion. K I N E M A T I C ANALYSIS: Analysis of the kinematic aspects of mechanisms. 2.2 Motion (Quantities, States) MOTION: Change in position and derivatives thereof of a body or system of bodies with respect to a reference frame and time. ABSOLUTE MOTION: Motion with respect to a fixed frame of reference. RELATIVE MOTION: Motion with respect to a moving frame of reference. INVERSE MOTION: Motion of a frame of reference relative to a moving body.

F R A M E MOTION (TRANSPORTATION): Motion of a moving system of reference. DISPLACEMENT: Change of position of a body with respect to a fixed reference frame. RELATIVE DISPLACEMENT: Displacement with respect to a moving reference frame. A N G U L A R DISPLACEMENT: Displacement of a rigid body in rotation. G E N E R A L I Z E D COORDINATE OF A MECHANISM: Corrdinate that represents a set of independent variables determining the positions of the links of a mechanism with respect to the frame. VELOCITY: Rate of displacement with respect to time. ABSOLUTE VELOCITY: Velocity with respect to a fixed frame of reference. F R A M E (TRANSPORTATION) VELOCITY: Absolute velocity of a particu!ar point of a moving frame of reference. RELATIVE VELOCITY: Velocity with respect to a moving reference frame. A N G U L A R VELOCITY: Rate of angular displacement with respect to time. G E N E R A L I Z E D VELOCITY OF A MECHANISM: Rate of change of generalized coordinate with respect to time. ACCELERATION: Rate of change of velocity with respect to time. N O R M A L ACCELERATION: Component of acceleration of a point normal to its velocity. T A N G E N T I A L ACCELERATION: Component of acceleration of a point collinear with its velocity. ABSOLUTE ACCELERATION: Rate of change of absolute velocity with respect to time. RELATIVE ACCELERATION: Rate of change of relative velocity with respect to time. F R A M E (TRANSPORTATION) ACCELERATION: Absolute acceleration of a particular point in a moving frame of reference. CORIOLIS ACCELERATION: Component of the absolute acceleration of a point in relative motion due to the angular velocity of the frame of reference. It equals twice the vector product of the angular velocity of the moving frame of reference and the relative velocity of the given moving point. A N G U L A R ACCELERATION: Rate of change of angular velocity with respect to time. RETARDATION: Tangential acceleration of a point with a sense opposite to that of the velocity of this point. JERK: 1. Rate of change of acceleration with respect to time. 2. Sudden change of acceleration. TRANSLATION: Motion of a rigid body in which each straight line rigidly connected with the body remains parallel to its initial direction. RECTILINEAR TRANSLATION: Translation in which the paths of the points of a rigid body are straight lines. ROTATION: Motion of a rigid body in which all points move on circles or arcs centred on the same axis.

Terminology for the Theory of Machines and Mechanisms A N G L E O F ROTATION: Angle turned through by any line rigidly connected with a rotating body and perpendicular to the axis of rotation. INFINITESIMAL ROTATION (ELEMENTARY A N G U L A R DISPLACEMENT): Rotation through a vanishingly small angle. PRECESSION: Rotation of a rigid body about an axis fixed in space when combined with a rotation about an axis fixed in the body, the two axes being concurrent. R E G U L A R PRECESSION: Precession with uniform rotations about the moving and fixed axes. NUTATION: Motion of a rigid body occurring simultaneously with a precession, when the angle between axes of rotation and precession varies in time. CENTRAL MOTION: Motion in which the direction of the acceleration of a point always passes through a fixed point (called the centre of motion). P L A N A R (PLANE) MOTION: Motion of a rigid body whose points describe curves located in parallel planes. SPATIAL MOTION: Motion of a rigid body when at least one of its points describes a spatial curve. SCREW MOTION: Spatial motion of a rigid body consisting of a translatory component parallel to a rotary one, the two components being related to each other. SPHERICAL MOTION: Spatial motion of a rigid body in which all points of the body move on concentric spheres. R O L L I N G MOTION: Relative angular displacement about a common tangent of two rigid bodies in contact. SPIN MOTION: Relative angular displacement about the common normal of two rigid bodies in contact. S L I D I N G MOTION: Relative displacement of the contacting points of two rigid bodies in the tangent plane at the point of contact. G E N E R A T I O N OF MOTION: Moving a rigid body against resistances by energy conversion. S T A R T I N G R E G I M E O F A MECHANISM: Regime of motion of a mechanism when the kinetic energy at the end of this regime is greater than at its beginning. STOPPING R E G I M E OF A M E C H A N I S M : Regime of motion of a mechanism when the kinetic energy at the end of this regime is less than at its beginning. STEADY M O T I O N O F A M E C H A N I S M : Motion of a mechanism when its kinetic energy is constant or is a periodic function of time with the frequency of motion. U N I F O R M MOTION: Motion with constant velocity. C O E F F I C I E N T O F N O N - U N I F O R M I T Y OF MOTION: Ratio of the difference between the maximum and minimum values of the generalized veloc-

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ity to its mean value during one period of the steady motion. PERIODIC MOTION: Displacement that varies periodically. PERIOD (OF A MOTION): The shortest interval of time or another independent variable after which the motion repeats itself. APERIODIC MOTION: Motion which is towards a position of equilibrium without oscillation. SIMPLE H A R M O N I C MOTION: Motion with a sinusoidal law of displacement. PHASE ANGLE: Instantaneous argument of a simple harmonic function. CHARACTERISTIC O F MOTION: Simplified representation of a motion showing only the sequence of intervals of motion, reversal of motion and intervals of rest. STEP MOTION: Unidirectional motion periodically interrupted by dwells. DWELL: State wherein a point or a link has zero or approximately zero velocity for a finite interval of time. INSTANTANEOUS (MOMENTARY) DWELL: State wherein a point or a link has zero velocity and acceleration for an infinitesimal interval of time. PILGRIM-STEP MOTION: Motion that is unidirectional with periodically recurring reversals. T R A N S F E R FUNCTION: Function describing the dependence of output motion upon input motion. TRANSMISSION RATIO: The input speed divided by output speed. G E A R RATIO: Transmission ratio for a gear train. D E A D POINT: Configuration for which the transmission ratio is infinite. LIMIT POSITION: Configuration for which the transmission ratio is zero. IDLE M O T I O N OF A LINK: Motion of a link when the working operation is not performed. LEAD (PITCH): Translational displacement of a screw during one complete revolution. PITCH: Translational displacement of a screw for one radian of rotation. LIFT: Linear displacement of a cam follower. 2.3 Kinematic geometry PATH (TRAJECTORY): The line which a moving point describes in a given system of reference. AXIS O F ROTATION: Straight line in a rotating rigid body whose points have zero displacement either in a finite time interval, or in an infinitesimal time interval, with respect to a frame of reference. INSTANTANEOUS CENTRE OF ROTATION: Point in a lamina moving in its own plane where the velocity, relative to a reference frame, is zero at a given instant. SCREW AXIS: Straight line in a rigid body whose points are displaced either in a finite time interval, or in an infinitesimal time interval, coaxially with the line itself. INSTANTANEOUS SCREW AXIS: Locus of the

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points in a rigid body in general spatial motion, whose linear velocity is parallel to the angular velocity vector of the body at a given instant. INSTANTANEOUS CENTRE OF ACCELERATION: Point in a lamina moving in its own plane where the acceleration is zero at a given instant. CENTRODE: Locus of the instantaneous centre of rotation in the relative planar motion of two laminae, described upon either one lamina or the other. FIXED CENTRODE: Locus traced on a fixed lamina by the instantaneous centre of rotation of a coplanar moving lamina. MOVING CENTRODE: Locus traced on a moving lamina by its instantaneous centre of rotation as the lamina moves in its own plane. CARDAN CIRCLES: Circular fixed and moving centrodes, the diameter of one being half that of the other. AXODE: Ruled spatial surface generated by the instantaneous screw axis for the relative motion of the body relative to another body described in either one body or the other. FIXED AXODE: Axode described in a fixed reference frame. MOVING AXODE: Axode described in a reference frame rigidly connected to the moving body. POLE: Centre of rotation for a finite or an instantaneous rotation of a lamina in its own plane. CENTRODE TANGENT: Common tangent to the centrodes at the instantaneous centre of rotation. POLE VELOCITY: Rate of change of the position of instantaneous centre of rotation with respect to time. VELOCITY HODOGRAPH: Curve described by the arrowhead of the velocity vectors of a moving point, when all the vectors are drawn from a common origin. BRESSE NORMAL CIRCLE: Locus of those points in a lamina moving in its own plane which have zero tangential acceleration at a given instant. INFLECTION CIRCLE: Locus of those points in a lamina moving in its own plane that are at points of inflection in their paths and so have zero normal acceleration at a given instant. INFLECTION POINT: Point in a path or curve where the radius of curvature is infinite. INFLECTION CENTRE: Point on the inflection circle through which pass all vectors of tangential accelerations of the points which lie on the inflection circle. CUBIC OF STATIONARY CURVATURE: Locus of points in a lamina moving in its own plane for which the path curvature is stationary at a given instant (a maximum or a minimum). CENTRING- (PIVOT-) POINT CURVE: Locus of the centres of curvature of the paths of points that lie on the cubic of stationary curvature. BALL POINT: Intersection between the inflection circle and the cubic of stationary curvature, other than at the instantaneous centre of rotation.

COUPLER POINT: Point in the plane of and attached to the coupler of a mechanism. COUPLER-POINT CURVE: Trajectory traced by a coupler point. POLE TRIANGLE: Triangle formed by joining the three poles of finite rotation of a lamina moving through three positions in its own plane. IMAGE (MIRROR) POLE: Reflection of a pole with respect to the side formed by the other two poles of the pole triangle. OPPOSITE POLE: The pole for the displacement of a lamina from any one position to another of four positions in its own plane is opposite to the pole for the displacement from one to the other of the remaining two positions. OPPOSITE-POLE QUADRILATERAL: Quadrilateral formed by joining two pairs of opposite poles from the six poles of finite rotation determined by a lamina moving through four positions in its own plane. CIRCLE POINT: Point in a lamina moving in its own plane which for four positions of the lamina lies on a fixed circle. CIRCLE-POINT CURVE: Locus of the circle points on the moving lamina. CENTRE POINT: Centre of the fixed circle drawn through the four positions of a circle point. CENTRE-POINT CURVE: Locus of the centre points with respect to the fixed frame of reference. 3. DYNAMICS

3.1 General DYNAMICS: Branch of theoretical mechanics dealing with the motion and equilibrium of bodies and mechanical systems under the action of forces. STATICS: Branch of theoretical mechanics dealing with the equilibrium of bodies under the action of forces. 3.2 Power quantities and characteristics FORCE: Action of its surroundings on a body tending to change its state of rest or motion. LINE OF ACTION OF A FORCE: Straight live along which the vector representing a given force lies. M A G N I T U D E OF A FORCE: Number of units of force obtained by comparing a given force with a standard, taken as unit force. ACTIVE (APPLIED) FORCE: Force capable of producing a motion. REACTION: Force arising in a constraint and acting upon a constrained body due to the action of an active force upon that body. NORMAL REACTION: Component of reaction perpendicular to the surface of a body. TANGENTIAL REACTION: Component of reaction tangential to the surface of a body. CENTRIPETAL FORCE: Reaction to a centrifugal force. INERTIA FORCE (D'ALEMBERT FORCE): Force due to the dynamic effect of the motion of a particle and which is in equilibrium with the resultant

Terminology for the Theory of Machines and Mechanisms of the active and reactive forces acting on the particle. It equals the product of the mass of the particle and the negative of its acceleration. C E N T R I F U G A L FORCE: Component of inertia force directed along the principal normal to the path of a particle. CORIOLIS FORCE: Component of inertia force equal to the product of the mass of a particle and the negative of its Coriolis component of acceleration. RELATIVE FORCE: Inertia force equal to the product of the mass of a particle and the negative of its acceleration relative to a moving frame of reference. T R A N S P O R T A T I O N FORCE: Inertia force equal to the product of the mass of a particle and the negative of its transportation acceleration. CENTRAL FORCE: Force whose line of action at all times and at every point in space passes through one fixed point (centre). EXTERNAL FORCE: Force due to the action of another body or system on the body or system under consideration. I N T E R N A L FORCE: Force acting upon a particle or set of particles of a given system, originating from another particle or set of particles in the same system. ELASTIC FORCE: Internal force arising in an elastically strained body. C O N C E N T R A T E D FORCE: Force whose action may be regarded as being applied at one point of a body. DISTRIBUTED FORCE (CONTINUOUS FORCE): Force which acts over a line, surface or volume of a body. BODY FORCE: Force which acts on the elements of the volume of a body. S U R F A C E FORCE: Force whose action is distributed over the surface or a part of the surface of a body. COMPRESSIVE F O R C E (IN BARS): Normal component of a force acting on a cross-section of a body and which is directed into the body. TENSILE F O R C E (IN BARS): Normal component of a force acting on a cross-section of a body and which is directed, out from the body. A X I A L F O R C E ( N O R M A L FORCE, LONGIT U D I N A L FORCE) (IN BARS): Component of internal force normal to a given cross-section of a bar. SHEARING FORCE (SHEAR FORCE, TRANSVERSE FORCE, L A T E R A L FORCE) (IN BARS): Component of a force acting on a crosssection of a body and lying in the plane of the cross-section. CRITICAL F O R C E (FOR A BAR IN COMPRESSION): Maximum compressive force that can be sustained by a bar in stable equilibrium. EQUIVALENT. F O R C E (REDUCED FORCE): Force applied in an arbitrary point of a mechanism such that its power equals the power of the given set of forces. B E A R I N G FORCE: Action of one link of a mechanism upon another at a bearing.

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S H A K I N G FORCE: Vector sum of all inertia forces of the moving links of a machine. IMPULSIVE FORCE: Force existing during an interval of time that is short compared to the time constant of the system to which it is applied. IMPULSE: Integral with respect to time of a force over the period during which it acts. DETERMINISTIC FORCE: Force that is fully determinable at any instant of time. STOCHASTIC FORCE: Force that is specified by a set of values with a probability varying, in general, from value to value. M O M E N T OF A FORCE ABOUT AN AXIS: Component along a given axis of the moment of a force about any point on this axis, M O M E N T O F A F O R C E ABOUT A POINT: Vector product of a radius vector from the point to the line of action of the force and the force itself, ARM O F A FORCE (MOMENT ARM): Shortest distance to the line of action of a force from a given point. M O M E N T O F A COUPLE: Vector sum of the moments about any point in space of the forces forming a given couple. RESULTANT MOMENT: Moment equal to the vector sum of the moments of all the forces of a system about a chosen point. B E N D I N G M O M E N T (OF A BAR): Component in the plane of a cross-section of the moments about its centroid of forces acting on that cross-section. F R I C T I O N A L MOMENT: Sum of the moments of the frictional forces in a journal or thrust bearing about the axis of rotation. TORSIONAL M O M E N T (TWISTING MOMENT, TORQUE): Component normal to the plane of a cross-section of the moments of forces acting on that cross-section about its centroid. INPUT TORQUE: Torque applied to driving (or input) link of a mechanism. OUTPUT TORQUE: Torque supplied by the output link of a mechanism. I N E R T I A COUPLE ( D ' A L E M B E R T COUPLE): Vector equal to the product of the moment of inertia of a body and the negative of its angular acceleration. M O M E N T U M (LINEAR MOMENTUM): Vector sum of the products of the velocities and masses of the individual particles of a material system. G E N E R A L I Z E D M O M E N T U M : Partial derivatives of the kinetic energy of a system with respect to a generalized coordinate. M O M E N T O F M O M E N T U M : Vector sum of the moments of momenta of the particles of a system about a given point or axis. A N G U L A R M O M E N T U M (OF A BODY): Vector equal to the product of the moment of inertia of a body and its angular velocity. EQUIVALENT FORCE SYSTEM: Set of forces whose resultant force and moment with respect to a chosen point equal those of the original set of forces. R E S U L T A N T FORCE: Vector sum of a set of forces.

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PARALLEL FORCE SYSTEM: Set of forces whose lines of action are parallel. COUPLE: Two parallel forces that are equal in magnitude, but opposite in sense. EQUIVALENT M O M E N T (REDUCED MOMENT): Couple applied to an arbitrary link of a mechanism such that its power equals the power of the given set of forces and couples. C O P L A N A R FORCE SYSTEM: Set of forces whose lines of action lie in one plane. C O N C U R R E N T FORCE SYSTEM: Set of forces whose lines of action intersect each other at one point. SPATIAL FORCE SYSTEM: Set of forces whose lines of action do not lie in one plane. WRENCH: Set of forces composed of a force and a couple whose vectors are parallel. EQUILIBRIUM: State of a system of forces and couples when the resultant force and the resultant couple of the system are simultaneously zero. B A L A N C I N G (OF A MECHANISM): Distribution of masses of the links so that the resultant force and couple exerted on the frame are constant. STATIC BALANCE (OF A R O T A T I N G BODY): Distribution of the mass of a rotor so that its centre of mass lies on its axis of rotation. D Y N A M I C BALANCE (OF A R O T A T I N G BODY): Distribution of the mass of a rotor so that the axis of rotation coincides with one of the principal axes of inertia. BALANCED MECHANISM: Mechanism for which the resultant force and resultant moment applied to the frame during the prescribed motion of initial links remain constant. LOAD: Set of active external forces acting upon a given link of a mechanism. CONTINUOUS LOAD (DISTRIBUTED LOAD): Load whose points of application continuously fill in a given segment or surface. U N I F O R M LOAD ( U N I F O R M L Y DISTRIBUTED LOAD): Distributed load whose magnitude per unit area or unit length is constant. DEAD LOAD (FIXED LOAD, P E R M A N E N T LOAD): Load consisting of forces whose values, directions and points of application, in relation to a given body, are invariant with respect to time. LIVE LOAD ( C H A N G I N G LOAD): Load consisting of forces whose values or directions or points of application vary with respect to time. D Y N A M I C LOAD: Load changing so fast that inertia forces are not negligible. A L T E R N A T I N G LOAD: Load varying periodically so that limiting load values are equal in absolute value, but opposite in sign. P U L S A T I N G L-OAD: Load varying periodically so that both of the limiting load values are of the same sign. T R A V E L L I N G LOAD ( R O L L I N G LOAD, MOVING LOAD): Load consisting of a set of forces which are constant in value and direction, but whose

points of application change their position in relation to the given body. F O L L O W E R LOAD: Load force whose direction varies with the deflection of the structure at the point of application. CRITICAL LOAD: Least load to cause the loss of stability of a structure. F I E L D OF FORCE: Region of space in which force is a function of position. FORCE FUNCTION: The function whose partial derivatives give the components of force in the direction of differentiation. CONSERVATIVE F I E L D OF FORCE: Field of force possessing potential. CONSERVATIVE FORCE: Force of a potential field of forces. NON-CONSERVATIVE FORCE: Force having a component dissipating energy from, or imparting energy to, a system. DISSIPATIVE FORCE: Force which, during the motion of a system, causes an increasing loss in the total (mechanical) energy of the system, due to its transformation into other forms of energy. G E N E R A L I Z E D FORCE: Quantity which, when multiplied by a virtual increment of the generalized coordinate gives the virtual work of all the forces of the system. R A Y L E I G H DISSIPATIVE F U N C T I O N (DISSIPATIVE FUNCTION): Function of generalized co-ordinates and generalized velocities of a system such that its partial derivatives with respect to the generalized velocities and reversed in sign equal the corresponding generalized dissipative forces. C A N O N I C A L VARIABLE ( H A M I L T O N I A N VARIABLE): Generalized co-ordinate and generalized moment. CYCLIC CO-ORDINATE (CYCLIC IGNORABLE): Generalized coordinate that does not appear explicitly in the function for the kinetic potential, but in the form of its derivative with respect to time. A P P A R E N T MOTION: Motion in which the noncyclic coordinates change. CONCEALED MOTION: Motion in which only the cyclic coordinates change. U N P E R T U R B E D MOTION: Motion of a system resulting from given forces and initial conditions. PERTURBED MOTION: Motion of a system differing slightly from a given motion (unperturbed motion) due to a change of initial conditions or other influences. I N I T I A L CONDITIONS: Displacements, velocities, etc. of a system at an instant of time taken as origin. H A M I L T O N I A N FUNCTION: Total (mechanical) energy of a system expressed through canonical variables. L A G R A N G I A N F U N C T I O N (KINETIC POTENTIAL): Difference between the kinetic energy and the potential energy of a system.

Terminology for the Theory of Machines and Mechanisms POTENTIAL E N E R G Y (OF A PARTICLE): Scalar quantity equal to the work done in a conservative force field in moving a particle from a given position to a reference position whose potential energy is conventionally taken to be zero. POTENTIAL E N E R G Y (OF A SYSTEM): Sum of potential energies of all particles of a material system. POTENTIAL E N E R G Y (OF AN ELASTIC BODY) [POTENTIAL E N E R G Y OF D E F O R MATION, ELASTIC POTENTIAL ENERGY, (ELASTIC) STRAIN ENERGY]: Work done by the internal forces of an elastic body in moving from its deformed state to the undeformed one for which the potential energy is conventionally taken to be zero. KINETIC E N E R G Y (OF A PARTICLE): Energy of motion. It equals -~t m y 2 for a particle of mass m and velocity v. KINETIC E N E R G Y OF A SYSTEM: Sum of kinetic energies of all particles of the system. M E C H A N I C A L E N E R G Y (TOTAL ENERGY): Sum of kinetic and potential energies. WORK: Integral of elementary work for a finite displacement. E L E M E N T A R Y WORK: Scalar product of a force and elementary displacement at its point of application. USEFUL WORK: Work done by the forces in overcoming the useful resistance. V I R T U A L WORK: The work done by a force in a virtual displacement of the point at which the force acts. W O R K O F D E F O R M A T I O N : Work done by the external forces during the deformation of a body. POWER: Rate of work with respect to time. POWER OF A F O R C E (ACTIVITY OF A FORCE): Rate of work of a force equal to the scalar product of the force and the velocity of its point of action. U S E F U L POWER: Rate of useful work with respect to time. EFFICIENCY. Ratio of the useful power to the input power. I N S T A N T A N E O U S E F F I C I E N C Y (OF A MECHANISM): Ratio of the useful power to the power of driving forces. CYCLIC E F F I C I E N C Y (OF A M E C H A N I S M ) [COEFFICIENT O F E F F I C I E N C Y (OF A MECHANISM)]: Ratio of the useful (effective power) to the power of driving forces during a cycle of the steadystate motion of the mechanism. 3.3 Principles PRINCIPLE O F ENERGY: Principle according to which the increase in kinetic energy of a system in a given interval of-time is equal to the work done by all the forces acting upon the system during the same interval. PRINCIPLE OF CONSERVATION O F (MECHANICAL) ENERGY: Principle according to which the mechanical (total) energy of a system M M T Vol. 18, No. 6

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moving in a conservative field of forces, remains constant. PRINCIPLE OF M O M E N T U M : Principle according to which the change in momentum of a system in a given interval of time is equal to the total impulse of the forces acting on the system in the same interval of time. PRINCIPLE O F CONSERVATION O F MOM E N T U M :Principle according to which the momentum of a system free of external forces, remains constant. PRINCIPLE OF M O M E N T OF M O M E N T U M (PRINCIPLE OF A N G U L A R MOMENTUM): Principle according to which the derivative with respect to time of the moment of momentum of a system about a given point or axis is equal to the sum of the moments of all the forces acting upon the system about this point or axis. PRINCIPLE O F CONSERVATION OF MOMENT OF M O M E N T U M , (PRINCIPLE OF CONSERVATION OF A N G U L A R MOMENTUM): Principle according to which the moment of momentum of a system is constant when the resultant moment of the external forces is zero. PRINCIPLE OF MOTION OF CENTRE O F MASS: Principle according to which the centre of mass of a system moves as if it were a particle having a mass equal to the mass of the whole system and as if all external forces of the system were acting at this point. SUPERPOSITION PRINCIPLE: Principle according to which the responses of a linear system to different excitations are additive. PRINCIPLE O F V I R T U A L WORK: Principle according to which the necessary and sufficient condition of equilibrium of a system is that the virtual work done by forces acting upon the system in an arbitrary virtual displacement is zero. D ' A L E M B E R T ' S PRINCIPLE: Principle according to which the actual forces and couples acting upon bodies of a system are in equilibrium with the inertia forces and couples of these bodies. H A M I L T O N ' S PRINCIPLE: Principle according to which the integral of the Lagrangian function with respect to time for actual motion attains a value which is extreme, when compared with all other possible conceivable motions of a given system. GALILEO'S LAW O F RELATIVITY: Law that states that every system of reference moving with respect to a given inertial system with uniform rectilinear translation is also an inertial system. LAW OF (UNIVERSAL) GRAVITATION: Law that states that every particle attracts every other particle with a force that is proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. NEWTON'S FIRST LAW (FIRST PRINCIPLE O F DYNAMICS, FIRST LAW OF MOTION): Law according to which a particle subject only to

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forces in equilibrium continues in its state of rest or uniform rectilinear motion. NEWTON'S SECOND LAW (SECOND PRINCIPLE OF DYNAMICS, SECOND LAW OF MOTION): Law that states that the product of the mass of a particle and its acceleration is at any given instant equal to the resultant force acting on this particle. NEWTON'S T H I R D LAW (THIRD PRINCIPLE OF DYNAMICS, T H I R D LAW O~ MOTION): Law which states that the forces of two particles acting on one another are equal in value, but opposite in sense, and lie on the line joining the two particles. 3.4 Structural characteristics DENSITY: In a homogenous body the ratio of the mass to the volume of the body. In a nonhomogeneous body the derivative of mass with respect to volume at a point of the body. ELASTICITY: Property of a body to recover its original shape and size after removal of the external forces causing the deformation. ELASTIC HYSTERESIS: Incomplete reversibility of the work of deformation occurring in solid bodies. Y O U N G ' S MODULUS OF ELASTICITY: Ratio of the change in stress to the change in strain for a material that obeys Hooke's law. HOOKE'S LAW: Law of proportionality between stress and strain that applies to linear-elastic materials. PLASTICITY: Property of a body to maintain permanent deformation after removal of the external forces causing the deformation. STIFFNESS: Measure of the ability of a body or construction to resist deformation due to the action of external forces. COMPLIANCE (FLEXIBILITY): Reciprocal of stiffness. STIFFNESS COEFFICIENT: Change of force (or torque) divided by the corresponding translational (or rotational) displacement of an elastic element ANISOTROPY: Variation of the physical properties in a body with direction. ISOTROPY: Independence of direction of the physical properties in a body. L O N G I T U D I N A L R I G I D I T Y (OF A BAR): Scalar quantity equal to the magnitude of force required to produce unit change of length in tension or compression. TORSIONAL R I G I D I T Y (OF A BAR): Scalar quantity equal to the magnitude of the torsional moment required to produce an unit angle of twisting. F L E X U R A L R I G I D I T Y (OF A BAR) (BENDING STIFFNESS): Scalar quantity equal to the bending moment required to produce unit change in curvature. MODULUS OF R I G I D I T Y (MODULUS OF ELASTICITY) IN SHEAR: Ratio of the change in shearing stress to the change in shearing strain.

STRAIN: Temporary or permanent change per unit length in a dimension of a body. ELASTIC STRAIN (ELASTIC DEFORMATION): Strain which disappears after removal of the static system of external forces causing it. PLASTIC STRAIN (PLASTIC DEFORMATION, P E R M A N E N T SET): Strain which does not disappear after removal of the static system of external forces causing it. AVERAGE STRAIN (UNIT ELONGATION): Ratio of the increase in the original length of an element to this length. TORSION (TWIST): State of strain and stress in the cross-section of a bar where the internal forces reduce to a couple with the moment vector perpendicular to the plane of the cross-section. STRAIN: Derivative of displacement. A N G L E OF TWIST (ANGLE OF TORSION) (OF A BAR): Angle of relative rotation of two cross-sections of a bar about the longitudinal axis. SHEAR STRAIN (ANGLE OF DEFORMATION: Change in angle between two straight lines drawn on a body, which are perpendicular before strain is applied. DEFLECTION (OF A BEAM): Displacement of points on the longitudinal axis of a beam in bending, in a direction normal to this axis. DEFLECTION (OF A PLATE): Displacement of a point in the middle surface of a plate in the direction normal to this surface. M O D U L U S OF A F O U N D A T I O N : Ratio of the pressure on linear-elastic foundation to the deflection it produces. MODULUS OF DEFLECTION (OF AN ELASTIC SUPPORT): See STIFFNESS. B U C K L I N G (OF A BAR): Bending of a straight bar in axial compression due to instability when the compressive forces exceed a critical value. EQUIVALENT (REDUCED) BUCKLING LENGTH (OF A BAR): Length of a bar, pin-jointed at its ends, which has the same cross-section and critical load as a given bar of the same material. SLENDERNESS RATIO (OF A BAR): Ratio of the equivalent buckling length of a bar to the radius of gyration of its cross-section with respect to the axis about which bending occurs during buckling. LATERAL B U C K L I N G (OF A BEAM): Loss of stability of a beam bent about one transverse axis, as a result of which bending occurs about another transverse axis. BISTABLE BUCKLING: Sudden transition of a deformed body from one form of stable equilibrium to another form of stable equilibrium wherein the points of the body undergo finite displacements. VIRTUAL D E F O R M A T I O N : Arbitrary deformation of a body. CONTACT AREA: Area of contact of two deformed bodies pressed together. STRESS: Limit of the ratio of surface force divided by the area on which it acts, as the area tends to zero. N O R M A L STRESS: Component of stress in the

Terminology for the Theory of Machines and Mechanisms direction normal to the element of surface on which the stress acts. SHEAR STRESS: Component of stress lying in the plane of the element of surface on which it acts. TENSION: State of stress in which the stresses acting on the ends of an element of a bar tend to extend that element. AXIAL TENSION: Tension in which the resultant force acts through the centroid of the cross-section of a bar. COMPRESSION: State of stress in which stresses acting on the ends of an element of a bar tend to reduce the length of that element. ULTIMATE STRENGTH: Limit of resistance of the internal forces in a solid body to external forces acting upon it. BENDING (OF A BAR): State of stress tending to change the curvature of the longitudinal axis of a bar. SHEARING (IN BARS): State of stress on a cross-section of a bar in which the shearing stresses have a non-zero resultant. SHEAR CENTRE (FLEXURAL CENTRE) (OF A BEAM): Point in cross-section of a beam in bending through which the resultant of the shearing stresses must pass for the angle of twist to be zero. CENTRE OF TWIST (OF A BAR): Point about which the cross-section of a bar in torsion rotates. ELASTIC AXIS (ELASTIC LINE) (OF A BEAM): Locus of the shear centres of the crosssections of a beam. N E U T R A L AXIS (OF A BEAM): Straight line which lies in the plane of the cross-section of a beam in bending and along which the normal stresses are zero. FRICTION: Complex of phenomena arising in the contact area of two contacting bodies causing tangential reaction, dissipation of energy, etc. SLIDING FRICTION: Friction occurring when sliding takes place between the surfaces of two bodies in contact. ROLLING FRICTION: Resistance to motion that occurs when a real deformable body is rolling. PIVOTING (SPINy FRICTION: Friction due to relative rotation of two bodies about the common normal at their point of contact. STATIC FRICTION: Friction occurring between two bodies that are at rest relative to each other. LIMITING FRICTION: Static friction force when slip is impending. KINETIC (SLIDING) FRICTION: Friction occurring in relative motion between two bodies in contact. FRICTIONAL FORCE: Tangential reaction acting against the relative movement of two bodies whose surfaces are in contact. COEFFICIENT OF FRICTION: Ratio of the magnitude of the limiting frictional force to the magnitude of the normal reaction. ANGLE OF FRICTION: Greatest possible angle between the reactions of two bodies and the common normal to their surfaces at the point of contact.

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CONE OF FRICTION: Conical surface within which the reactions between two bodies in contact must lie. MECHANICAL SHOCK (IMPULSE): Excitation in the form of a sudden change in force, position, velocity or acceleration. IMPACT: Sudden contact of short duration between two bodies. IMPACT FORCE: Force arising in contacting bodies during impact. CENTRAL IMPACT: Impact in which the impact forces pass through the centres of mass of the colliding bodies. ECCENTRIC IMPACT: Impact in which the impact forces do not pass through the centres of mass of the colliding bodies. DIRECT IMPACT: Impact in which the relative velocities of the centres of mass of the bodies are in the direction of the common normal to their surfaces at the point of contact. OBLIQUE IMPACT: Impact in which the relative velocities of the centres of mass of the bodies are not in the direction of the common normal to their surfaces at the point of contact. L O N G I T U D I N A L IMPACT (OF A BAR): Impact where the impact force is along the centre line of the bar. TRANSVERSE IMPACT (OF A BAR): Impact where the impact force is perpendicular to the centre line of the bar. ELASTIC IMPACT: Impact in which only elastic deformation occurs at the place of contact between the two colliding bodies. INELASTIC IMPACT: Impact in which only plastic deformation occurs in the region of contact of the two colliding bodies. COMPRESSION PERIOD: Interval of time during which the impact forces are increasing. RESTITUTION PERIOD: Interval of time during which the impact forces decrease to zero. COEFFICIENT OF RESTITUTION: Ratio of the impulse of the impact force in the restitution period to the impulse of the impact force in the compression period. CENTRE OF PERCUSSION: Point in a body through which the line of action of an impact force must pass normal to a fixed axis about which the body can rotate if the impulsive reaction at the axis of rotation is to be zero. ATTRACTION: Tendency to draw particles together caused by forces acting from one particle upon another. GRAVITATION: Property of mass expressing itself in the mutual attraction of bodies. FORCE OF GRAVITY (GRAVITY FORCE): Force of attraction arising from the law of gravitation. WEIGHT: Magnitude of the force of gravity on a body. GRAVITATIONAL FIELD: Field of force in which the force acting upon a particle is gravitational.

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CENTRE OF GRAVITY: Point in a body through which the resultant of the gravitational forces on its component particles acts. ACCELERATION DUE TO GRAVITY: Acceleration produced by the force of gravity. (Note: By international agreement, the value g = 9,806 m/s 2 has been chosen as the standard acceleration due to gravity). GYROSCOPIC EFFECT (GYROEFFECT, GYROSTATIC ACTION): Inertial effect arising from a forced steady precession of a gyroscope. 3.5 Dynamical systems BODY: Collection of particles, whose relative positions are related, which may be regarded as one whole having the form of a line, surface or solid. RIGID BODY: Theoretical model of a solid body in which the distances between particles are considered to be constant, regardless of the forces acting upon the body. ELASTIC BODY: Body that is able to sustain elastic deformation. HOMOGENEOUS BODY: Body whose physical properties are the same at all points. ISOTROPIC BODY: Body within which physical properties are independent of direction. HETEROGENEOUS BODY. Body whose physical properties are not the same at all points. BAR (ROD): Body whose dynamical behaviour can be adequately represented by considering its mass to be concentrated along a line. CABLE (STRING): Flexible bar, capable of transmitting of tensile forces only. STRUT (COLUMN): Straight bar subjected to compression. CURVED BAR: Bar whose centre line in an unloaded state, is curved. ARCH: Curved bar acting primarily in compression. SPRING: Elastic body shaped so that it can suffer substantial elastic deformation. TRUSS (FRAME-WORK): System of bars connected at their ends to form a rigid structure. BEAM: Bar loaded with forces perpendicular to its centre line. SIMPLY-SUPPORTED BEAM: Beam on two supports which prevent transverse movement only. CONTINUOUS BEAM: Beam resting on three or more supports. CANTILEVER BEAM: Beam having one end built-in and the other end free. SPAN (OF A BEAM): Distance between the two adjacent points of support of a beam. GRID (GRILLAGE): Two or more sets of parallel beams with all the beams in one plane and the axes of the sets intersecting. THICK PLATE: Plate whose thickness is of the same order as other dimensions. THIN PLATE: Plate whose thickness is small compared with all other dimensions.

MEMBRANE: Thin plate or shell with negligible flexural rigidity. MIDDLE SURFACE (OF A PLATE): Surface which bisects the thickness of a plate at every point. DISK (CIRCULAR PLATE): Plate whose middle surface is circular in shape. CYLINDRICAL SHELL: Shell whose middle surface is cylindrical. SANDWICH STRUCTURE: Beam, plate or shell constructed in three layers, the properties of the middle layer being different from those of the outer layers. MULTI-LAYERED STRUCTURE: Beam, plate or shell which has two or more layers with different physical properties. SUPPORT: Type of constraint. FIXED SUPPORT: Support which renders a given point of a body immovable. MOVABLE SUPPORT: Support which confines the movement of a given point of a body to one direction only. SMOOTH SUPPORT: Support whose reaction has only a normal component. FREE (SIMPLE) SUPPORT: Support allowing only a rotation about a particular axis. ELASTIC SUPPORT: Support which deflects elastically under the pressure of the body supported. ROLLER SUPPORT: Support allowing a rotation around an axis and a rectilinear translation in a direction perpendicular to that axis. FOUNDATION: Supporting structure. ELASTIC FOUNDATION: Elastic body constituting a continuous support for a beam or plate. SIMPLE PENDULUM: Particle suspended on a perfectly flexible, inextensible, weightless thread moving under gravity with periodic motion in a vertical plane. SPHERICAL PENDULUM: Particle suspended on a perfectly flexible, inextensible, weightless thread moving with periodic motion on the surface of a sphere. COMPOUND PENDULUM: Rigid body free to turn about an horizontal axis, moving with periodic motion under the action of the forces of gravity. DOUBLE PENDULUM: Two pendula hinged together so that one provides a moving support for the other. GYROSCOPE: Rigid cylindrical body rotating about a fixed point, having an angular velocity about the central axis that is large in comparison with remaining components of angular velocity. PARTICLE (MASS POINT, MATERIAL POINT): Geometrical point to which a finite mass is assigned. MASS (OF A PARTICLE): The amount of material in a particle as measured by the force necessary to cause unit acceleration of the particle. MASS OF A BODY: Sum of the masses of the particles that make up the body. CENTRE OF MASS: Point in a body or system of particles such that the sum (integral) taken over all

Terminology for the Theory of Machines and Mechanisms the particles, of the vector drawn from the point in question to each particle and multiplied by the mass of the particle, is zero. EQUIVALENT (REDUCED) MASS O F A MECHANISM: Mass to be attached to a particular point in a mechanism so that its kinetic energy is equal to the sum of the kinetic energy of all links in the mechanism. M O M E N T OF INERTIA: Scalar quantity equal to the sum (integral) of the products of the masses of the individual particles (elements of mass) of a solid body and the squares of their distances from a given axis. POLAR M O M E N T OF I N E R T I A O F A LAMINA: Scalar quantity equal to the sum (integral) of the products of the masses of the individual particles (elements of mass) of a lamina and the squares of their distances from the pole. POLAR M O M E N T OF I N E R T I A O F A BODY: Moment of inertia of an axi-symmetric body about its axis of symmetry. PRODUCT OF I N E R T I A (MOMENT OF DEVIATION): Scalar quantity equal to the sum (integral) of the products of the masses of individual particles (elements of mass) of a solid body and their distances from two mutually perpendicular planes. P R I N C I P A L AXES O F INERTIA: Three mutually perpendicular axes intersecting each other at a given point with respect to which the products of inertia of a solid body are zero. PRINCIPAL M O M E N T OF INERTIA: Moment of inertia about a principal axis of inertia. INERTIA TENSOR: Symmetrical tensor whose components for a rigid body are 3 moments of inertia and the negatives of 3 products of inertia about the axes of a system of coordinates, fixed in the body. EQUIVALENT (REDUCED) M O M E N T OF INERTIA (OF A MECHANISM): Moment of inertia assigned to a reference link about its axis of rotation so that the kinetic energy of this link is equal to the total kinetic energy of all the actual links of a given mechanism. RADIUS OF GYRATION: Distance from a pole or axis at which the mass of a body may be assumed to be concentrated so as to have the same moment of inertia as the actual body about the given pole or axis. ELLIPSOID OF I N E R T I A ( M O M E N T A L ELLIPSOID, POINSOT ELLIPSOID OF INERTIA): Locus of the ends of vectors measured from a given point on every axis passing through this point, the lengths of the vectors being inversely proportional to the radii of gyration. C E N T R A L ELLIPSOID OF I N E R T I A (MOMENTAL ELLIPSOID AT CENTRE OF GRAVITY): Ellipsoid of inertia for the centre of mass. POLHODE: For a rotating rigid body subject to no external resultant torque, the line of intersection of the cone traced out by the angular velocity vector with the momental ellipsoid.

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HERPOLHODE: Locus on a fixed plane of the point of contact of the momental ellipsoid rolling thereon while undergoing Poinsot motion. CENTROID: Point whose coordinates with respect to any point of cartesian axes are the mean values of the points of the given figure (curve, surface or solid). CENTRAL AXIS (OF A BAR): Locus of centroids of the cross-sections of a bar. SYSTEM: Assemblage of components acting as a whole. M E C H A N I C A L SYSTEM: System in which the main properties are mass, stiffness and damping. P L A N A R SYSTEM (COPLANAR SYSTEM): System capable of being loaded and moving in one definite plane only. SPATIAL SYSTEM: System capable of being loaded by a spatial force system and/or moving in three-dimensional space. DISCRETE SYSTEM (MULTI-DEGREE-OFF R E E D O M SYSTEM, LUMPED P A R A M E T E R SYSTEM): System which requires only a finite number of generalized coordinates to specify its configuration. CONSTRAINT: Restriction on the motion of a system. U N I L A T E R A L CONSTRAINT: Requirement that a particular variable should be not less than a given datum value, or alternatively, that it should not be greater than a given datum value. BILATERAL CONSTRAINT: Constraint expressed by equations linking the coordinates of the particles of a system (and possibly their derivatives with respect to time) and time. G E O M E T R I C CONSTRAINT: Constraint whose equations depend only on coordinates of the points of a system and, possibly, on time. D I F F E R E N T I A L CONSTRAINT: Constraint whose equations depend not only on coordinates of the points of a system but also on their first derivatives with respect to time and, possibly, on time. R H E O N O M I C CONSTRAINT: Constraint that is dependent on time. SCLERONOMIC CONSTRAINT: Constraint that is independent of time. H O L O N O M I C CONSTRAINT: Geometric constraint or a differential constraint whose equations are integrable. N O N - H O L O N O M I C CONSTRAINT: Differential constraint whose equations are not integrable. HOLONOMIC SYSTEM: Constrained system for which all constraints are holonomic. N O N - H O L O N O M I C SYSTEM: Mechanical system with at least one non-holonomic constraint. R H E O N O M I C SYSTEM: Constrained system in which at least one constraint depends on time. SCLERONOMIC SYSTEM: Constrained system in which all the constraints are independent of time. I N V A R I A N T SYSTEM: System in which the distances between individual particles are invariant. STATICALLY D E T E R M I N A T E SYSTEM: Sys-

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tem for which the distribution of internal forces is determined by the principles of statics alone. STATICALLY I N D E T E R M I N A T E SYSTEM (HYPERSTATIC SYSTEM): System in which the distribution of internal forces depends on the material properties of the members of the system. LINEAR SYSTEM: System in which the magnitude of the response is proportional to the magnitude of excitation. CONTINUOUS SYSTEM (CONTINUUM): System in which physical properties are continuously distributed. VARIABLE-MASS SYSTEM: System whose total mass may change in time due to the addition or subtraction of mass. EQUIVALENT SYSTEM: System that may be substituted for another system for the purpose of analysis. INERTIAL SYSTEM: System of reference in which the basic principles of classical mechanics hold. SEISMIC SYSTEM: System consisting of a mass attached to a reference base by one or more flexible elements. DEGREE OF F R E E D O M (OF A M E C H A N I CAL SYSTEM): Number of independent generalized coordinates required to define completely the configuration of a system at any instant of time. M E C H A N I C A L MOBILITY: Complex ratio of generalized velocity at a point in a linear mechanical system to generalized force at the same or another point in the same system during simply harmonic motion. DIRECT MOBILITY (DRIVING-POINT MOBILITY): Complex ratio of generalized velocity and generalized force taken at the same point in a linear mechanical system during simple harmonic motion. DIRECT RECEPTANCE: Ratio of the displacement at a point in a system to a simple harmonic exciting force applied at the same point and in the same direction. CROSS RECEPTANCE: Ratio of the displacement at one point in a system to a simple harmonic excitation at another point. EQUILIBRIUM: State of a system in which all forces are counterbalanced by equal and opposite forces. STABLE EQUILIBRIUM: State to which a system stays arbitrarily close for all time after a sufficiently small disturbance has been applied. UNSTABLE EQUILIBRIUM: State of equilibrium from which a system tends to move indefinitely after the application of vanishingly small disturbance. N E U T R A L EQUILIBRIUM: State where a system can remain in equilibrium at rest after a sufficiently small displacement. EQUATIONS OF EQUILIBRIUM: Mathematical expression of the conditions of equilibrium. EQUILIBRIUM CONFIGURATION: Geometrical form of a material system in which the forces acting upon it are in equilibrium.

ENVIRONMENT: Aggregate of all external conditions and influences to which a system is subjected. VIRTUAL DISPLACEMENT: An arbitrary infinitesimal displacement of a particle or system from a given state. EXCITATION (STIMULUS): Time dependent external force (or other input) whereby energy is imparted to a system. COMPLEX EXCITATION: Harmonic excitation that is represented by a complex number. COMPLEX RESPONSE: Response of a linear system to a complex excitation, or the response of a damped system to a harmonic excitation. S U B H A R M O N I C RESPONSE: Response of a mechanical system exhibiting some of the characteristics of resonance at a frequency having a period which is an integral multiple of the period of the excitation. TRANSMITTANCE: Ratio of the Laplace transform of the output to that of the input. TRANSMISSIBILITY: Nondimensional ratio of the response amplitude of a system in steady-state forced vibration to the excitation amplitude. The ratio may be one of forces, displacements, velocities, or accelerations. D Y N A M I C STIFFNESS (DYNAMIC SPRING CONSTANT): Ratio of the amplitude of exciting force to the amplitude of displacement during harmonic forced vibration of a linear system. IMPEDANCE: Ratio of harmonic input of a linear system to its output expressed in complex form. PROCESS: Collection of signals, the properties of which being considered with respect to time. R A N D O M PROCESS (STOCHASTIC PROCESS): Set (ensemble) of time functions that can be characterized through statistical properties. STATIONARY PROCESS: Ensemble of timehistories such that their statistical properties are invariant with respect to time. ERGODIC PROCESS: Stationary process involving an ensemble of time-histories where time averages are the same for every time-history. STATIONARY STATE (SELF-STATIONARY): State of a random signal in which the averages over sufficiently long, but finite, time intervals are independent of the time at which the sample is taken. 3.6 Vibrations VIBRATION: Mechanical oscillation. PERIODIC QUANTITY: Any quantity subject to periodic changes. FREQUENCY: Number of periods occurring in unit time. F U N D A M E N T A L F R E Q U E N C Y (OF A PERIODIC QUANTITY): Reciprocal of the fundamental period. CYCLE: Whole sequence of the periodic quantity during one period. OSCILLATION: Variation usually with time, of the magnitude of a quantity about its mean value. AMPLITUDE: 1. Greatest deviation of the instan-

Terminology for the Theory of Machines and Mechanisms taneous value of the periodic quantity from its mean. 2. Maximum value of a simple harmonic quantity. SIMPLE HARMONIC QUANTITY (SIN U S O I D A L QUANTITY): Periodic quantity that is a sinusoidal function of the independent variable. H A R M O N I C (OF A PERIODIC QUANTITY) ( H A R M O N I C COMPONENT, F O U R I E R COMPONENT): Sinusoid whose frequency is an integral multiple of the fundamental frequency. SUBHARMONIC: Sinusoidal quantity whose period is an integral multiple of the fundamental period of the quantity to which it is related. U L T R A H A R M O N I C : Sinusoidal quantity whose frequency is an integral portion of the fundamental frequency of the quantity to which it is related. SPECTRUM: Set of quantities characterizing harmonic components expressed as a function of frequency or wavelength. PEAK-TO-PEAK VALUE (OF A N OSCILL A T I N G QUANTITY): Algebraic difference between the extreme values of a quantity. H A R M O N I C VIBRATION (SINUSOIDAL VIBRATION): Vibration in which the motion is a sinusoidal function of time. FUNDAMENTAL VIBRATION: Harmonic component of a vibration with the lowest frequency. PERIODIC VIBRATION: Vibration in which all the characteristic quantities recur over the same equal increments of time. STEADY-STATE VIBRATION: Continuing periodic vibration. ALMOST-PERIODIC VIBRATION (QUASIPERIODIC VIBRATION): Vibration which deviates only slightly from a periodic vibration. T R A N S I E N T VIBRATION: Vibratory motion of a system other than steady state. R A N D O M VIBRATION: Vibration whose magnitude cannot be precisely predicted for any given instant of time. FREE VIBRATION: Vibration over a period of time of a system free from excitation. N O R M A L VIBRATIONS: Free vibrations in one of normal modes. F O R C E D VIBRATION: Vibration of a system caused by a sustained excitation. SYNCHRONOUS VIBRATION: Vibrations having the same frequency. BEAT: Periodic variation of the amplitude of vibration with time, arising from the superposition of two sinusoidal vibrations with slightly different frequencies. L O N G I T U D I N A L VIBRATIONS (OF BARS): Vibrations in which points of a bar move in a direction parallel to its centre line. TRANSVERSE VIBRATIONS (OF BARS): Vibrations in which bending occurs in the bar. T O R S I O N A L VIBRATIONS (OF BARS): Vibrations in which torsion occurs in the bar. MODE OF VIBRATION: Configuration of the displacements of characteristic points of a system from their mean positions when the system is under-

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going periodic vibration at any time other than when all the deflections are zero. N O R M A L MODE (OF VIBRATION) (NATU R A L MODE, CHARACTERISTIC MODE, EIGENMODE, P R I N C I P A L MODE, M O D A L VECTOR, PROPER VECTOR, LATENT VECTOR): Mode of free harmonic vibration of a linear system vibrating at one of its natural frequencies. F U N D A M E N T A L MODE: Normal mode of vibration associated with the lowest natural frequency of a vibrating system. COUPLED MODES: Modes of vibration that are not independent but which influence one another because of energy transfer from one mode to another. U N C O U P L E D MODES: Modes of vibration that can exist in a system concurrently with, and independently of, other modes, no energy being transferred from one mode to another. NODE: Stationary point of a mode of periodic vibration or a standing wave. (Note: An entirety of such points forms nodal lines or nodal surfaces). ANTINODE: Point of a mode of periodic vibration or a standing wave for which the peak-topeak value attains the maximum with respect to neighbouring points. Note: An entirety of such points forms antinodal lines or antinodal surfaces. F U N D A M E N T A L F R E Q U E N C Y (OF A VIB R A T I N G SYSTEM): Lowest natural frequency of a system. RESONANCE: State in which the frequency of an excitation coincides with the frequency of an undamped natural frequency causing the amplitude of vibration to become large. RESONANCE FREQUENCY: Frequency of a forced vibration of which resonance occurs. CRITICAL SPEED: Characteristic speed, such that resonance of the system occurs. QUALITY F A C T O R (Q-FACTOR): Quantity which is a measure of the sharpness of resonance, or frequency selectivity of a resonant oscillatory system (mechanical or electrical) having a single degree of freedom. L O G A R I T H M I C DECREMENT: Natural logarithm of the ratio of any two successive maxima of like sign, in the decay of a single-frequency oscillation. N A T U R A L FREQUENCY: Frequency of free vibration resulting from only elastic and inertia forces of a linear system. D A M P I N G : Any influence which tends to dissipate the energy of a system. L I N E A R VISCOUS D A M P I N G (VISCOUS DAMPING): Dissipation of energy that occurs when the relative motion of two elements of a vibration system is resisted by a force whose magnitude is proportional to the relative velocity and in a direction opposite to the direction of the relative velocity. EQUIVALENT VISCOUS D A M P I N G : Linear viscous damping, assumed for the purpose of analysis of a vibratory motion, such that the dissipation of

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energy per cycle is the same as it is for the actual, damping. D A M P I N G COEFFICIENT: Coefficient of proportionality between the damping force and relative velocity. D A M P I N G RATIO (FRACTION OF CRITICAL DAMPING): Ratio of the actual damping coefficient to the critical damping coefficient. NON-LINEAR VISCOUS D A M P I N G : Damping for which the force is a function of relative velocity, other than simple proportionality, and which tends to zero as the relative velocity tends to zero. CRITICAL D A M P I N G : Amount of viscous damping that corresponds with the limiting condition between an oscillatory and non-oscillatory decay of free motion. WAVE: Change in physical state which is propagated through a medium. TRANSVERSE WAVE: Wave in which the direction of disturbance to the medium is perpendicular to the direction of propagation of the wave. L O N G I T U D I N A L WAVE: Wave in which the direction of disturbance to the medium is parallel to the direction of propagation. SHEAR WAVE: Wave which is propagated as a result of shear stresses. SHOCK WAVE: Shock motion (displacement, pressure, or other variable) associated with the propagation of the shock through a medium or structure and characterized by a wave front at which a finite change in strain occurs over an infinitesimal distance. COMPRESSION WAVE: Wave which is propagated as a result of compressive or tensile stresses in elastic medium. S T A N D I N G WAVE: Periodic wave having a fixed amplitude distribution in space. WAVE FRONT: Locus of points of a progressive wave having the same phase at a given instant. (Note: Wave front for a surface wave is a continuous line, for a space wave a continuous surface). WAVELENGTH (OF A SINUSOIDAL WAVE): Distance between two successive points, in the direction of propagation which are separated by one period.

4. MACHINE CONTROL AND MEASUREMENTS

4.1 Signals and Functions CONTROLLED VARIABLE: Quantity or condition in a process which is intended to be measured and controlled. M A N I P U L A T E D VARIABLE: Quantity or condition which the automatic controller applies to the controlled system. REFERENCE INPUT: Signal established as a standard to be lbllowed by controlled variables for a feedback control system, by virtue of its relation to the command. BIAS: Constant reference which fixes the operating

point or the point of initial response in a particular device. C O M M A N D : Input which is established or varied by some means external to the automatic control system under consideration. F R E Q U E N C Y - M O D U L A T E D SIGNAL: Signal where information is contained in the deviation from a centre frequency. P R I M A R Y FEEDBACK: Signal which is a function of the controlled variable and which is compared with the reference input. A C T U A T I N G SIGNAL: Difference between the reference input and the primary feedback signal. F R E Q U E N C Y RESPONSE: Steady-state ratio of the magnitude and the difference in phase of the output to a sinusoidal input for a system. A C T U A T I N G S I G N A L RATIO: Frequency response of the actuating signal to the reference input. CONTROL RATIO: Frequency response of the controlled variable to the reference input. GAIN: Ratio of magnitude of the output to the magnitude of the sinusoidal input for a system. LOOP RATIO: Frequency response of a system whose output is primary feedback and input is the actuating signal. LOOP PHASE: Phase of loop ratio. LOOP GAIN: Magnitude of loop ratio. G A I N MARGIN: Loop gain of stable system at the frequency of phase crossover. G A I N CROSSOVER: Point in the plot of loop gain at which the magnitude of loop gain is unity. PHASE CROSSOVER: Point in the plot of loop gain at which the phase angle is rad. PHASE M A R G I N : Supplement of the loop phase angle of a stable system at the frequency of gain crossover. TIME RESPONSE: Output of a system as a function of time, following the application of a prescribed input. RESPONSE TIME: Time required for the output of a system first to reach a specified value after the application of a step input of disturbance. RISE TIME: Time required for the output of a system to increase from one specified percentage of the final value to another, following the application of a step input. SETTLING TIME: Time required for the absolute value of the difference between the output of a system and its steady-state value to become and remain less than specified amount, following the application of a step input. STEP FUNCTION: Function which is zero for all values of time prior to certain instant and a constant for all values of time thereafter. ZERO SUPPRESSION: Technique of suppressing part of an incoming signal so that the rest may be amplified and displayed with greater magnification on a recorder chart. D Y N A M I C RUN: Test performed on an instrument to obtain the overall behaviour and to establish

Terminology for the Theory of Machines and Mechanisms or corroborate specifications such as frequency response and natural frequency of the device. AMPLITUDE RESPONSE: Maximum output amplitude obtainable at points over the frequency range of an instrument operating under rated conditions. ATTENUATION: Reduction or division of signal amplitude while retaining the characteristic wave° form. DECAY: Unintentional or intended attenuation of changing quantites above (or below) a certain point. LAG (DELAY): Interval of time by which a particular phase of one waveform follows the corresponding phase of another. 4.2 Accuracy and Errors ACCURACY: Capability of an instrument to follow the true value of a given phenomenon. PRECISION: Degree of reproducibility among several independent measurements of the same true value under specified conditions. SENSITIVITY: Property of an instrument that determines scale factor. GAIN STABILITY: Extent to which the sensitivity of an instrument remains constant with time. REPEATABILITY: Maximum deviation from the mean of corresponding data points taken from repeated tests under identical conditions. DRIFT: Gradual and unintentional deviation of a given property of an indicating instrument, usually the deviation from zero rest position. INSTABILITY (DYNAMIC DRIFT): Maximum change in sensitivity from initial value over a stated period of time under stated conditions. ZERO LINE STABILITY: Absence of drift when an indicating instrument is at zero. RESOLUTION: Smallest change in applied stimulus that will produce a detectable change in the instrument output. INFINITE RESOLUTION: Resolution capable of stepless adjustment. THRESHOLD SENSITIVITY: Lowest level of the controlled variable which produces effective response of automatic controller or instruments. DEAD BAND: Range of values through which the input of a system can be varied without initiating output response. SYSTEM ERROR: Difference between desired and actual value of the controlled variable. S T R U C T U R A L ERROR: Difference, due to approximations in design, between the function actually generated by a mechanism and the one that it was required to generate. OVERSHOOT (UNDERSHOOT): Maximum (minimum) of the transient response of a system caused by varying the input from one steady value to another. TOTAL OVERSHOOT: Maximum value of the system error for a specified stimulus. TRANSIENT ERROR: Difference between the

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instantaneous system error and steady-state error for a specified stimulus. TRANSIENT OVERSHOOT: Maximum value of the transient error. STEADY-STATE ERROR: Error that remains after the transient has expired. COMBINED ERROR: Largest possible error in an instrument resulting from a combination of adverse conditions. OFFSET ERROR: Constant error in the input of a device as a result of which input is not zero when output is zero. STATIC ERROR BAND: Spread of error that would be present if the indicator of a readout device were to stop at some deflection. DYNAMIC ERROR BAND: Spread or band of output-amplitude deviation incurred by a constantamplitude sinewave as its frequency is varied over a specified part of the frequency spectrum. CALIBRATION: Process of comparing a set of discrete magnitudes or the characteristic curve of a continuously varying magnitude with another set or curve previously established as a standard. PRIMARY CALIBRATION: Calibration procedure in which the instrument output is observed and recorded while the input is applied under precise conditions. CALIBRATION CURVE: Path or locus of a point which moves so that its coordinates on a graph are corresponding values of input signals and output deflections. RANGE: Upper and lower limits between which an input may be applied to an instrument and for which the instrument is calibrated. FULL SCALE: Total interval over which an instrument is intended to operate. BANDWIDTH: Range of frequencies over which a given device is designed to operate within specified limits. SCALE FACTOR: Ratio of real to analogue values. OPERATING TEMPERATURE: Temperature (or range of temperatures) over which in instrument is expected to operate. SPAN: Reach or spread between two established limits such as the difference between high and low values of physical measurements. DISTORTION: Unwanted change in waveform.

4.3 Devices and Components CONTROL ELEMENT: Components required to produce the manipulated variable or the actuating signal. AUTOMATIC CONTROLLER: Device which measures the value of a controlled variable and operates to correct it to a selected constant or timevarying value. FEEDBACK ELEMENT: Components required to produce the primary feedback from the controlled variable.

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CONTROL SYSTEM OF AN A U T O M A T I C MACHINE: System securing the succession of displacements of each operating member in accordance with the given program. A U T O M A T I C CONTROL SYSTEM (FEEDBACK CONTROL SYSTEM, CLOSED-LOOP CONTROL SYSTEM): Any operable arrangement of one or more automatic controllers connected with one or more processes. SERVOSYSTEM: Feedback control system in which the reference input is a function of time. SERVOMECHANISM: Servosystem in which the controlled variables is a mechanical quantity. REGULATOR: Feedback control system which primary concern is to keep the value of the controlled variable constant. GOVERNOR: Regulator used to keep the speed of an engine constant. ABSORBER: Device used to reduce the magnitude of a shock or vibration. DAMPER: Absorber which operates by the dissipation of energy. DETUNER: Device that modifies the vibration characteristics of the system to which it is attached. D Y N A M I C VIBRATION R E D U C E R (TUNED REDUCER): Device for reducing vibrations of a system over a particular frequency range by transfer of energy to an auxiliary resonant system. SNUBBER: Device used to increase the stiffness of an elastic system (usually by a large factor) whenever the displacement becomes larger than a specified amount. VERNIER: Any device, control, or scale used to obtain fine adjustment or more accurate measurement than is practicable with the main measuring scale. TRANSDUCER: Device for translating faithfully the changing magnitude of one kind of quantity into corresponding changes of another kind of quantity. ACTIVE TRANSDUCER: Transducer that has an auxiliary source of power which supplies a major part of the output power while the input signal supplies only an insignificant portion. PASSIVE TRANSDUCER: Transducer whose output energy is supplied entirely or almost entirely by its input signal. DISPLACEMENT TRANSDUCER: Transducer whose output is proportional to the displacement input. VELOCITY TRANSDUCER: Transducer whose output is proportional to the velocity input. ACCELEROMETER: Transducer whose output is proportional to the acceleration input. STROBOSCOPE: Light source that can be adjusted to flash at the desired rate. INTERFEROMETER: Optical device in which a beam of light is divided into two parts which travel different paths and recombine to form interference fringes. GROUND: Point in a circuit used as a common reference or datum point for measuring voltages.

SENSOR: Device for sensing, selecting and transmitting of signals for control purposes. 4.4 R o b o t control COOPERATIVE CONTROL: Control of several manipulators working simultaneously on one job. SENSORY CONTROL: Control by the feedback of sensory information. CHARACTERISTIC POINT: Certain point of the handled object or hand used to describe its motion. CONTINUOUS-PATH CONTROL: Control of a characteristical point to follow a predetermined path continuously. POINT-TO-POINT CONTROL: Control of a characteristic point to take up a series of predetermined positions sequentially. TEACH-IN P R O G R A M M I N G : Programming a manipulator by taking it manually through a sequence of operations. POSITIONAL ACCURACY: Degree of coincidence between the required and actual positions. PLAYBACK ACCURACY: Degree of coincidence between the position taught and the playback position. OBJECT RECOGNITION: Discrimination of a particular object from others and its environments. PATTERN M A T C H I N G : Comparison of two patterns to determine whether or not they belong to the same class.

APPENDIX: GENERAL TERMS USED IN T M M

SCALAR (SCALAR QUANTITY): Any quantity that is completely specified by one real number. VECTOR: 1. Directed line segment. 2. Matrix of n rows and a single column (or of n columns and a single row). VECTOR QUANTITY: Quantity which, in addition to being geometrically represented by a vector also adds in accordance with the parallelogram triangle rule. ABSOLUTE VALUE O F A VECTOR: Length of the line segment representing the vector. VECTOR FIELD: Region in which every point has a definite vector assigned to it. VECTOR FUNCTION: Relationship which determines a vector for every particular value of a scalar parameter. GRADIENT: Vector whose components along the axes ~/rectangular system of coordinates at a given point are equal to the partial derivatives of a given (scalar) function of the coordinates. POTENTIAL: (Scalar) Function whose gradient is the opposite vector to the vector of a given vector field. M A X I M U M VALUE ( M A X I M U M MAGNITUDE): Value of a function when any small change of the independent variable causes a decrease in the value of the function.

Terminology for the Theory of Machines and Mechanisms PEAK VALUE (PEAK MAGNITUDE): Maximum value of a quantity during a given interval. (Note: A peak value of an oscillating quantity is usually taken as the maximum deviation of that quantity from the mean value). MEAN-SQUARE VALUE: Average of the squared values of a function over a given interval. ROOT-MEAN-SQUARE VALUE (r.m.s. VALUE): Square root of the mean-square value. TIME HISTORY: Magnitude of a quantity expressed as a function of time. TIME CONSTANT (RELAXATION TIME):

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Time taken by an exponentially decaying quantity to decrease in magnitude by a factor e -1 = 0.3679. PARAMETER: Quantity that defines a property of a system. SIGNAL: Disturbance used to convey information. INPUT: Signal entering a system. OUTPUT: Signal issuing from a system. NOISE: Class of sounds, generally of a random nature, which do not exhibit clearly defined frequency components.