Mechanism design for legged locomotion systems

CHAPTER 1

Mechanism design for legged locomotion systems Giuseppe Carbonea, Marco Ceccarellib a

DIMEG, University of Calabria, Rende, Italy LARM2: Laboratory of Robot Mechatronics, Department of Industrial Engineering, University of Rome Tor Vergata, Rome, Italy b

1 Introduction Locomotion is defined as the “Movement or the ability to move from one place to another” [1]. More in particular in IFToMM terminology [2], it is defined as “autonomous, internally driven change of location of human being, animals, or machines during which base of support and center of mass of the body are displayed” with more details in the several types of locomotion as per the environment in which it is performed. Locomotion is fundamental to the survival of many animal species including humans. The mechanics and performance of locomotion varies significantly as function of the environment in which locomotor behaviors are executed, which can be divided into terrestrial, aquatic, aerial, as outlined in refs. [3–6]. Terrestrial locomotion can be achieved with legs, wheels, and crawlers. Legged locomotion is the most widely used solution for terrestrial locomotion in nature as it is the most effective speedy and versatile when it operates in a rough terrain or in presence of obstacles. The energy efficiency of legged locomotion might significantly vary among animals and machines. Wheeled/crawler locomotion is instead preferred for vehicles on flat surfaces as it can be more easily controlled, and it can be more energy efficient. A large literature reports a wide range of legged locomotion systems, which have been designed for a wide variety of applications as indicated for example in refs. [7, 8]. For example, there are legged locomotion systems, which are used for entertainment purposes; other solutions for carrying heavy loads on hills or rough terrains, or even for carrying humans while overcoming stairs or other architectonic barriers. The common limits of legged locomotion systems are high costs and complex design and operation, which often prevent a widespread in the market, even if they have been Design and Operation of Human Locomotion Systems https://doi.org/10.1016/B978-0-12-815659-9.00001-9

© 2020 Elsevier Inc. All rights reserved.

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Design and operation of human locomotion systems

inspired by very successful examples in nature. Accordingly, efforts should be made to improve user-friendliness, user-printed design and operation, costs of the solutions for legged locomotion systems, with activities since the very early design stage. Generally, legged systems can be slow and more difficult to design and operate with respect to mobile machines that are equipped with crawlers or wheels. But, legged robots are more suitable for rough terrain, where obstacles of any size can appear. In fact, the use of wheels or crawlers limits the size of the obstacle that can be climbed, to half the diameter of the wheels. On the contrary, legged machines can overcome obstacles that are comparable with the size of the machine leg. This chapter provides useful considerations for the design of legged locomotion systems by focusing at their mechanism synthesis for specific applications with suitable low-cost user-friendly features. After a general overview on design requirements and design process, several examples are reported as based on over 20 years of experiences by the authors.

2 Characteristics of legged locomotion Legged locomotion is the basis for several different types of movement such as walking, running, and jumping. Walking and running, in which the body is carried well off the surface on which a body is moving (substrate), occur only in arthropods and vertebrates. Running (cursorial) vertebrates are characterized by elongated lower legs and feet and by reduction and fusion of toes. Saltatory locomotion, movement by leaping, hopping, or jumping, is found in a number of insects and vertebrates. Only arthropods (e.g., insects, spiders, and crustaceans) and vertebrates have developed a means of rapid surface locomotion. In both groups, the body is raised above the ground and moved forward by means of a series of jointed appendages, the legs. Because the legs provide support as well as propulsion, the sequences of their movements must be adjusted to maintain the body’s center of gravity within a zone of support; if the center of gravity is outside this zone, the animal loses its balance and falls. It is the necessity to maintain stability that determines the functional sequences of limb movements, which are similar in vertebrates and arthropods. The apparent differences in the walking and slow running gaits of these two groups are caused by differences in the tetrapodal (four-legged) sequences of vertebrates and in the hexapodal (six-legged) or more sequences of arthropods. Although many legs increase stability during locomotion, they also

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appear to reduce the maximum speed of locomotion. Whereas the fastest vertebrate gaits are asymmetrical, arthropods cannot have asymmetrical gaits, because the movements of the legs would interfere with each other. The cycle of limb movements is the same in both arthropods and vertebrates. During the propulsive, or retractive, stage, which begins with footfall and ends with foot liftoff, the foot and leg remain essentially stationary as the body pivots forward over the leg. During the recovery, or protractive, stage, which begins with foot liftoff and ends with footfall, the body remains essentially stationary as the leg moves forward. The advance of one leg is a step; a stride is composed of as many steps as there are legs. During a stride, each leg passes through one complete cycle of retraction and protraction, and the distance that the body travels is equal to the longest step in the stride. The speed of locomotion is the product of stride length and duration of stride. Stride duration is directly related to retraction: the longer the propulsive stage, the more time is required to complete a stride and the slower is the gait. A gait is the sequence of leg movements for a single stride. For walking and slow running, gaits are generally symmetrical—i.e., the footfalls are regularly spaced in time. The gaits of fast-running vertebrates, however, tend to be asymmetrical—i.e., the footfalls are irregularly spaced in time. For example, the different gaits of insects are based on the synchrony of leg movements on the left (L) and right (R) sides of the animal. The wave of limb movement for each side passes anteriorly; the posterior leg protracts first, then the middle leg, and finally the anterior leg, producing the sequence R3 R2 R1 or L3 L2 L1. There is no limb interference, because the legs of one side do not have footfalls along the same longitudinal axis. The slowest walking gait of insects is the sequence R3 R2 R1 followed by the sequence L3 L2 L1. As the rate of protraction increases, the protractive waves of the right and left sides begin to overlap. Eventually, the top speed is reached when the posterior and anterior legs of one side move synchronously. This gait occurs because the protraction times for all legs are constant, the intervals between posterior and middle legs and between middle and anterior legs are constant, and the interval between posterior and anterior legs decreases with faster movements. Other gaits are possible in addition to those indicated above by altering the synchrony between left and right sides. The limb movements of centipedes and millipedes follow the same general rules as those of insects. The protraction waves usually pass from posterior to anterior. Because each leg is slightly ahead of its anteriorly adjacent leg during the locomotory cycle, one leg touches down or lifts off slightly before its anteriorly adjacent one. This coordination of limb movement produces

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metachronal waves, the frequency of which equals the duration of the complete protractive and retractive cycle. The length of the wave is directly proportional to the phase lag between adjacent legs. Cursorial (running) vertebrates are characterized by short, muscular upper legs and thin, elongated lower legs. This adaptation decreases the duration of the retractive–protractive cycle, thereby increasing the animal’s speed. Because the leg’s cycle is analogous to the swing of a pendulum, reduction of weight at the end of the leg increases its speed of oscillation. Cursorial mammals commonly use either the pace or the trot for steady, slow running. The highest running speeds, such as the gallop, are obtained with asymmetrical gaits. When galloping, the animal is never supported by more than two legs and occasionally is supported by none. The fastest runners, such as cheetahs or greyhounds, have an additional no-contact phase following hind foot contact. In cursorial birds and lizards, both of which are bipedal, the feet are enlarged to increase support and the body axis is held perpendicular to the ground, so that the center of gravity falls between the feet or within the foot-support zone. The running gait is, of course, a simple alternation of left and right legs. In lizards, however, bipedal running must begin with quadrupedal (four-footed) locomotion. As the lizard runs on all four legs, it gradually builds up sufficient speed so that its head end tilts up and back, after which it then runs on only its two hind legs. The structure of the legs can be very different among different types of animals in term of anatomy but the kinematic design and functioning can be recognized with common characters that can be summarized in having a foot with a space mobility of at least three d.o.f.s and an ovoid-like trajectory of foot reference point with the step size S and step height H, as shown in Fig. 1. In particular, such a kinematic design of a leg can be characterized by a spherical joint S at the hip articulation and revolute joints R at knee and ankle articulations. The step size gives the capability of the locomotion motion, while the step height H gives indication of overpassing obstacles. Both parameters can be increased on purpose during operation, but H is the main characteristic of a leg that makes legged systems very flexible, mainly in environments crowded with obstacles. The foot of a leg has the function of contact and interaction with the ground in order to provide a proper action and reaction in locomotion, both for force exchange and stable positioning. The peculiarities of foot anatomy and operation are also significant in differentiating and specializing animals for the specific environments in which they usually operate. The anatomy of

Mechanism design for legged locomotion systems

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Fig. 1 Main characteristics of a anthropomorphic leg: (A) Kinematic design; (B) foot point path.

legs in nature can be summarized with a bone structure with joint articulations, a complex system of muscles, and a complex neurological system. In replicating leg anatomy and functionality in walking robots, bone structure is often used as a reference structure for kinematic design with motion properties for smooth operation, payload capability, and nature-like actions. Design problems for leg mechanisms can be outlined by tackling the mechanics of robots, as in ref. [9]. Mechanical design aspects can be formulated by using models like the one in Fig. 2, in attaching the following problems: - design compactness and light weight - motion synchronization for step size and lift height - balancing actions and dynamics response - ground-foot contact and impact - actuation and forward velocity

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Fig. 2 A scheme for conditions in leg design overpassing an obstacle: (A) Sagittal plane; (B) front view.

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- motion planning (also for obstacle avoidance) - sensored and controlled interactions during walking - payload capacity and environment interaction. The problems for overcoming obstacle can be formulated with conditions referring to the schemes in Fig. 2, when referring to climbing a step as or for obstacle overpass. The static equilibrium gives the necessary conditions for walking and overcoming obstacles of the maximum allowed step height. In a sagittal plane the equilibrium can be expressed referring to Fig. 2A as a aL Rh
P
PL  0 g g (1) Rv
P
PL  0 Rv dR
PdP
PLðdP + dLÞ
CinS  0 where Rh and Rv are the horizontal and vertical components of R contact reaction; P is robot weight; PL is leg weight; a is motion acceleration and g is the gravity; dL, dR, and dP are the indicated distances; CL is the torque actuating a leg; CinS is the sagittal component of the inertial torque due to waist balancing movement. Point Q is considered the foot contact point about which the system will rotate in a possible fall. In the front plane, the equilibrium condition can be expressed referring to Fig. 2B as aS 0 g aS Rv
P  0 g Rv pR
PpP
PLðpP + pLÞ
Cinl  0 Rl
P

(2)

where Rl is the lateral component of R; aS is the lateral acceleration of robot body; Cinl is the lateral component of the inertial torque of waist balancing movement. Point S is the foot contact point about which the system will rotate in a possible fall. The components Rh and R1 refer to friction actions at the foot contact area. By using Eqs. (1), (2) conditions can be formulated for design and operation features that are useful to overcome obstacles of height h. From geometric viewpoints the obstacle/step of height h can be overpassed when the leg moves with the condition l1 ð1
cos ϕ1 Þ + l2 ð1
cosϕ2 Þ > h

(3)

in which l1 and l2 are the lengths of leg body links, whose angles ϕ1 and ϕ2 are given with respect to a vertical line. The design problem for overpassing obstacles can be formulated by using conditions like those in Eqs. (1)–(3) to properly size the leg links, and to give proper mobility ranges and actions of the leg operation.

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3 Existing legged locomotion systems The first ideas to design and implement legged locomotion vehicles date back to very old times. Since ancient times devices have been designed for transportation of passengers and materials, often with the use of animals. In addition to load transportation (including carrying passengers), there have been challenges for locomotion purposes, with attempts to replicate and/or mimic solutions in nature, as seen with a large variety of animals. Transportation systems were developed mainly as wheeled systems that are today very successful in vehicle technology. Readers can refer to corresponding literature for the history of vehicles, like cars, trucks, motorcycles and so on. With the development of Robotics, locomotion systems and walking machines have received stronger and stronger attention, with a large number of inventions and designs mainly within the last three decades. But most of the concepts and even structural designs have evolved, even unconsciously, from past solutions. Historical studies have been published on the evolution of walking machines in general, also within the history of robotics, whose literature is reported with basic references, like for example in refs. [10–12]. In modern times, two leading researchers Ichiro Kato and Miomir Vukobratovic achieved pioneering works in the field of legged robots in early 70s. Namely, Kato and his team at Waseda University, Tokyo, in Japan achieved the first anthropomorphic walking robot, WABOT 1, which was demonstrated in 1973, as reported in ref. [13]. In parallel, Vukobratovic and his team at the Mihailo Puppin Institute, Belgrade, Yugoslavia, designed the first active legged exoskeletons together with the related Zero Moment Point theory, as celebrated in ref. [14]. In the recent past several walking machines have been developed for several different purposes mainly in research laboratories. Significant examples of walking machines are shown in Figs. 3–13: - Honda robot ASIMO, Fig. 3A; - Sony robot SDR-4X, Fig. 3B; - Waseda robot WABIAN-RV, Fig. 3C; - Waseda biped locomotor WL-16R, Fig. 4; - CSIC robot RIMHO2, Fig. 5A; - Ambulatory Robotic Lab. robot Scout II, Fig. 5B; - Hirose & Yoneda Robotic Lab. robot TITAN VIII, Fig. 6A; - Intelligent Machines and Special Robotics Institute robot WorkPartner, Fig. 6B; - Chiba University COMET II, Fig. 7A;

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Fig. 3 Examples of current biped walking machines: (A) Honda robot ASIMO; (B) Sony Robot SDR-4X; (C) Waseda robot WABIAN-RV.

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Fig. 4 Waseda biped locomotor WL-16R with non anthropomorphic legs: (A) a side view; (B) carrying a human.

Mechanism design for legged locomotion systems

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Fig. 5 Examples of four-leg walking machines: (A) RIMHO2; (B) Scout II.

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Fig. 6 Examples of four-leg walking machines with wheels: (A) TITAN VIII; (B) WorkPartner.

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Fig. 7 Examples of six-leg walking machines: (A) COMET II; (B) RHex.

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Design and operation of human locomotion systems

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Fig. 8 Examples of six-leg walking machines for outdoor applications: (A) Walking forest machine; (B) Adaptive Suspension Vehicle.

Fig. 9 The low-cost four-leg robot AIBO.

- Ambulatory Robotic Lab. robot Rhex, Fig. 7B; - Plustech Ltd. Walking Forest Machine, Fig. 8A; - Ohio State University Adaptive Suspension Vehicle, Fig. 8B; - Sony robot AIBO, Fig. 9. ASIMO (Advanced Step in Innovative MObility), Fig. 3A, has been built by Honda company in Japan in the year 2000. It is a biped humanoid robot with 26 actuate degrees of freedom. Its size, weight and ranges of mobility have been designed to mimic as much as possible a human child and to move

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Start

Find out all the existing design solutions

Design specifications

Step1 Conclude the topological characteristics

Generalization

Principles and Rules of Generalization

Step2 The generalized chain

Number synthesis

Algorithm of number synthesis

Step3 Atlas of generalized kinematic chain

Specialization

Design requirements and constraints

Step4 Atlas of feasible specialized chains

Particularization Step5 Atlas of designs

Step6

Exclude existing designs

Atlas of new designs

End

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Fig. 10 Flowcharts for design procedure of locomotion legged systems: (A) a topology search design; (B) a general scheme.

freely within human living environments. ASIMO is able to ascend and descend stairs, to walk by following different patterns, to avoid obstacles, to grasp objects, to interact with humans by means of sound and image recognition. It is equipped with on board batteries for a continuous operating time of about 30 min.

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Fig. 11 The so-called Chebyshev-linkage leg developed at LARM: (A) a first prototype; (B) a kinematic diagram.

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Fig. 12 Simulation results for the walking characteristics of the 1-DOF leg in Fig. 11 with p ¼ 20 mm and h ¼
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Mechanism design for legged locomotion systems

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Fig. 13 Simulation results for the walking characteristics of the 1-DOF leg in Fig. 11 with p ¼ 20 mm and h ¼
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SDR-4X (Sony Dream Robot version 4X), Fig. 3B, has been built at Sony in the year 2002. It is a small biped humanoid robot that has been designed for entertainment purposes. It has a total of 38 degrees of freedoms. It can walk on irregular pavement (up to 10 mm) and tilted surface (up to 10°) and can prevent falling when an external pressure is applied. Image and sound recognition features have been also included in its capacities. It is equipped with on board batteries for a continuous operating time of 2 h approximately. WABIAN-RV (Waseda Biped humANoid Refined V), Fig. 3C, is a biped humanoid robot that has been developed for human-robot cooperation work at Waseda University, in Tokyo in the year 2002. It is the last version of WABIAN series started since 1972 [15]. It has a total of 43 dofs. The size and motion range of each link has been designed to be as human like as possible. A variety of walking modes are operated as dynamic forward and backward walking, marching in place, dancing, carrying a load, and

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emotional walking. Its software includes an on-line pattern generator, image and sound recognition features. It requires an external power supply. WL-16R (Waseda-Leg No.16 Refined), Fig. 4, has been designed at Waseda University in Tokyo in the year 2004. It is composed of two 6-dof legs with parallel architecture design. It is a bipedal robot with only lower limbs that can dynamically walk independently. Its upper body can be added by users according to their use purposes. In particular, it would be applicable to the welfare field as a walking wheelchair or as a walking support machine that is able to walk up and down stairs carrying or assisting a human. It is equipped with an on-board Nickel Metal Hydride battery for a continuous operating time of 1 h approximately. The RIMHO II walking robot, Fig. 5A, has been developed from the Industrial Automation Institute-CSIC and the CIEMAT in Madrid since 1993. It is a quadruped-walking machine of the insect type. Its four legs are based on a three-dimensional Cartesian pantograph mechanism. The RIMHO walking robot can perform both discontinuous and wave gaits over irregular terrain including slopes and stairs and has been tested also over natural terrZain. SCOUT II, Fig. 5B, has been developed at Ambulatory Robotic Laboratory in Montreal since 1998. It is composed of four legs. Each leg has one active degree of freedom only. A spring and a passive knee are added in order to provide two additional passive degrees of freedom for each leg. These passive degrees of freedom make the Scout II capable of achieving dynamic running similar to gallop and trot. SCOUT II is fully autonomous having on board power, computing and sensing. Other features include an on-board pan-tilt camera system and laser sensors. TITAN VIII, Fig. 6A has been built at Hirose & Yoneda Robotic Lab. in Tokyo in the year 1996. TITAN VIII is a walking machine having four legs. The leg mechanism is composed of a planar two degrees of freedom mechanism and a rotating mechanism which rotates this planar mechanism. Wires and pulleys are used for the power transmission within the leg. The feet of TITAN VIII can be used also as wheels in order to achieve faster motion on flat surfaces. WorkPartner, Fig. 6B, is a four leg mobile robot that has been built at the Intelligent Machines and Special Robotics Institute in Helsinki in 2000. The locomotion system of WorkPartner is hybrid. In fact, it is possible to move by means of legs only, with legs and wheels powered at the same time or with wheels only. WorkPartner is equipped with two arms having three degrees of freedom arms and a two-degree of freedom camera head. Several

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sensors have been installed on board such as potentiometers, force sensors, inclinometers, gyro, accelerometers, ultrasonic sensors, laser scanner. A combustion engine and four batteries are also installed on board for a continuous operating time of 30 min approximately. COMET II in Fig. 7A has been developed at Chiba University in Tokyo in 2002. It can be used as fully autonomous system or teleoperated by a human for demining tasks. It is equipped with two manipulators that are used for mine detection and grass cutting. Several sensors are installed on board such as metal detector, radar, cameras, force sensors, potentiometers. The implemented software includes obstacle avoidance features. Power supply is provided by a gasoline power generator for outdoor operation or from an external power supply for indoor laboratory tests. RHEx robot, Fig. 7B, has been developed at Ambulatory Robotic Lab. in Montreal since 1999. It has six legs with only one degree of freedom. The leg has a very simple design. It is made by heat shaped Delrin rods and it has a soft foot at its free end. RHEx robot is equipped with gyros accelerometers, and optical encoders. It is capable of achieving a wide variety of dynamically dextrous tasks, such as walking, running, leaping over obstacles, climbing stairs. Two batteries are on board installed for a continuous operating time of about 10 min. The Walking Forest Machine, Fig. 8A, has been developed at Plustech Ltd. since 1995 for outdoor forest harvesting tasks. It is composed of six articulated legs. It can move forward, backward, sideways and diagonally. It can also turn in place and step over obstacles. Depending on the irregularity of the terrain, the operator can adjust both the ground clearance of the machine and height of each step. The operator-friendly controls are incorporated in a joystick that controls direction of movement, traveling speed, step height and gait, and the ground clearance. Adaptive Suspension Vehicle, Fig. 8B, has been developed at Ohio State University since early 80s. It is composed of six articulated legs. Each leg has three active degrees of freedom. It has been designed for walking on rough terrains by carrying a maximum load of over 2000 N. It is equipped with gyros, laser sensors and a computer vision system that is used for adapting the gait to the environment. It can work either in teleoperated or operator-on-board mode by using active compliance control algorithms. AIBO robot in Fig. 9 is a four-leg robot for entertainment purposes. It has been developed by Sony since early 90s and is available on the market since 2003 at a price of about 2000 Euros. Its design has four legs with three degrees of freedom each. It is equipped with two microphones, a speaker,

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touch sensors, infrared sensors, accelerometers that provide AIBO with very high human-robot interaction capabilities. Rechargeable batteries are on board installed allowing for a continuous operating time of 1.5 h, approximately. The reported examples in Figs. 3–9 give an overview of the variety of walking systems that have been developed all around the world with different solutions for different applications. It is worth noting that most of them (with the exception of AIBO) are not yet available in the market but they are under further development in Research Labs. Generally, legged systems can be slow and more difficult to design and operate with respect to machines that are equipped with crawlers or wheels. But legged robots are more suitable for rough terrain, where obstacles of any size can appear. In fact, the use of wheels or crawlers limits the size of the obstacle that can be climbed, to half the diameter of the wheels. On the contrary, legged machines can overcome obstacles that are comparable with the size of the machine leg. Therefore, hybrid solutions that have legs and wheels at the same time have been also developed as shown for example in Fig. 6A and B. This type of walking machines may range from wheeled devices to true walking machines with a set of wheels. In the first case, the suspensions are arms working like legs to overcome particularly difficult obstacles. In the second case wheels are used to enhance the speed when moving on flat terrain.

4 Design considerations for legged locomotion systems Challenging design problems concerning traditional subjects for overall robot design can be specifically indicated for locomotion legged systems in - mechanical efficiency, for mechanical transmission and actuating power - light design, with large payload and limited size - static accuracy, for better grasping configurations - dynamic response, for controlling impulsive actions and balanced dynamics In addition, new problems can be identified for new solutions in - topological mechanism structures, for new enhanced designs - materials, for better mechanical design and environment interaction - tribology issues, for reduction of wear and longer accurate functioning with limited friction - energy sustainable solutions, for better attention to energy saving and recycling of wasted components

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The short above lists are aimed to indicate that new issues and reconsiderations of past experiences, even with more subjects, will be the challenges in the future mechanism design for legged mobile robots within increased mechatronic components. Future developments and more widespread use of walking machines may depend on the enhancement of leg design in the many mechatronic aspects that can be approached with new perspectives and technologies. Challenges and trends for designing leg mechanisms will be focused on improvements mainly in compact design, efficiency, payload capability, flexibility and environment impact and they can be attached mainly in the following topics: - topology of mechanism structures - formulation for high-speed computation - light compact mechanical design - interactions with environments and users or operators - advanced sensorization - adaptable control systems - smart materials and components - anthropomorphic and nature-inspired solutions for friendly user-oriented solutions The above considerations emphasize expected advances in traditional performance, but perhaps new applications will be invented for walking machines as a function of the new technology that will be made available in the future. In addition, future developments and applications will generate the rise of new problems and new emerging topics from other fields. A final aspect to be considered can be considered not only nature-like designs but developments beyond standard solutions. As per kinematic design of leg mechanisms, a design procedure may include not only the traditional dimensional synthesis for given data referring to motion requirements, as not only for foot point and body. Traditional techniques of mechanism design (synthesis) can be used when formulating the design problem properly as motion guiding problem, as reported for example in refs. [16, 17]. A specific topology search procedure can be proposed for the development of a conceptual design by looking to all the feasible mechanism structures as summarized in Fig. 10A, consisting of six steps as in ref. [18]. Step 1: Finding out all the existing design solutions that can fully satisfy required design specifications for locomotion and tasks and identifying the topological characteristics of these existing designs. Step 2: Selecting one of these existing solutions and transforming it into its corresponding generalized

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Design and operation of human locomotion systems

chain according to predetermined rules of generalization. Step 3: By using an algorithm for number synthesis, synthesizing an atlas of generalized chains that have the same number of links and joints as the generalized chain obtained in step 2. Step 4: By using a suitable algorithm of specialization, assigning links and joints to each generalized chain generated in step 3 in order to obtain an atlas of all the feasible specialized chains that satisfy the design specifications and constraints. Step 5: Particularizing each feasible specialized chain obtained in step 4 into its corresponding mechanical design to get an atlas of mechanical devices. Step 6: Identifying and excluding existing designs from the atlas of mechanical devices obtained in step 5, to get an atlas of new feasible designs satisfying required design specifications. The above design considerations and challenges can be summarized in a general design procedure like the one in Fig. 10B, in which the mechanical design of a locomotion legged system is a key aspect since the mechanical nature of the locomotion, although the design solution is an integrated solution of several other components with a mechatronic structure and operation. In particular, a design procedure can be started with a proper deep analysis and identification of the locomotions aims and the characteristics of the environment and tasks for which the system is designed. The conceive of a conceptual design may be outlined form different activity, including previous experiences and looking at the existing solutions. This wı`can be considered a starting point of a new design with challenges in matching the prescribed requirements and expected results, even beyond the given data. For this purpose, it is convenient to look for an optimized solution that can be obtained from several specific approaches. Form the authors’ experience the topology search can be considered useful to investigate all the possible solution that can be derived from the conceptual design also with the possibility to find new design ideas. This is part of the creative design activity that can give challenging results in identifying solutions that are beyond just the given data. Once the topology structure is chosen for the design developments the other activities can be carried out sequentially, as indicated in the flowchart in Fig. 10B with traditional or innovative procedures. Thus, the dimensional design can be worked out using the algorithms of kinematic synthesis and then the mechanical structure can be shaped in all its components with CAD designs and simulations. After having the mechanical structure defined the legged system can be completed with the equipment and corresponding software making it with the necessary abilities and flexibility. Thus, in this phase the sensors,

Mechanism design for legged locomotion systems

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control devices, computer facilities and other equipment as required for the task and environment can be chosen or even designed on purpose for the locomotion system under development. The complete design of a legged locomotion system as a robot system can be developed with a mechatronic design in which all the components and aspects are integrated in giving the necessary features of motion, sensing, reactintin and so on. After the design is defined a check of the performance can be worked out through simulation with numerical results and also through testing activities to characterize the built prototype. The construction of the prototype may require adjustments and manufacturing problems up to finalize the design process with a validation giving the characteristic data of the solution and usually a demo is used both to confirm practically the obtained results and to exhibit the prototype for possible applications and exploitations. In the flowchart of Fig. 10B it is indicated that after each phase a check is planned to verify the design progress and in case changes are required in the previous phases as in an iterative process towards an optimal solution that will consider all the possibilities for a final improved solution. In each of these phases, peculiarities of the attached problems and used approaches can lead to different solutions by looking both to the mechanics of locomotion and mechatronic design of a solution.

5 Illustrative examples Illustrative examples are reported from the direct experience of the authors with systems that they developed in the last two decades. At LARM locomotion legged systems were conceived, designed, and tested by looking at mechanical robotic design with features of low-cost solutions and easy operation. In the following main solutions are discussed to show those experiences with the aim to indicate the experience in developing legged locomotion systems.

5.1 Biped robot with Chebyshev-linkage legs Basic considerations for a low-cost leg design can be outlined as referring to the facts that the leg should generate an approximately straight-line trajectory for the foot point with respect to the body; the leg should have an easy robust mechanical design; and it should have the minimum number of DOFs to ensure the motion capability. At LARM the so-called Chebyshevlinkage leg has been developed with the above features as in ref. [19].

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The designed leg mechanism is shown in Fig. 11 with its mechanical design that is based on a Chebyshev four-bar-linkage, a five-bar linkage, and a pantograph mechanism. For such a mechanism, the leg motion can be performed by using one actuator only. The leg has been designed by considering compactness, modularity, light weight, reduced number of DOF as basic objectives to achieve the walking operation. Numerical and experimental results show that proper walking features can be obtained when points C and P in Fig. 11 are not coincident. The main characteristic of the proposed leg design consists in a fully-rotative actuation at point L to obtain the suitable trajectory of point B with one motor only that run continuously without any speed regulation. Furthermore, the trajectory of point B, and consequently, point A can be suitably modified by changing the design parameters. In particular, better features can be obtained if the transmission angles γ1 and γ2 have suitable values. Dimension of the leg prototype in Fig. 1 are 400 mm high, 40 mm  250 mm so that the leg has a maximum lift of 80 mm and the step is of 470 mm. In Figs. 12 and 13 the basic operation features of the Chebyshevpantograph leg mechanism are reported in terms of simulation results to show the feasibility of the low-cost easy operation design that have been experienced successfully by using a commercial DC motor without motion control equipment, since the capability of full rotatability of the crank link m. The computed walking motion sequences of the single DOF biped robot in Fig. 11B with the leg mechanism in Fig. 11A in a biped walking gait are shown in Figs. 14 and 15. Fig. 14 shows the computed motion sequence of the biped robot in sagittal and horizontal planes where the dashed line represents the left leg and the solid line represents the right leg. The right foot grasps the ground and the left leg swings in the air. Two configurations are shown in the figure with actuation angle α1 ¼ 270° and α1 ¼ 90°. In Fig. 14B the triangles represent the right foot and the rectangles represent the left foot in the horizontal plane. A black circle represents that the foot grasps the ground and the corresponding leg is in the propelling phase, otherwise it represents the foot in the air and the leg is in a non-propelling phase. A logic flowchart of the walking gaits for the biped robot is listed in Fig. 15 as per motion programming purposes with the two leg mechanisms operating sequentially in propelling and non-propelling phases to obtain a proper forward motion of the biped robot.

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Fig. 14 Motion sequences of walking for biped in Fig. 11B: (A) in sagittal plane; (B) in horizontal plane.

Fig. 15 Flowchart for the walking gait of the biped robot in Fig. 11B as referring to Fig. 14.

Fig. 16 shows the snapshots of the walking sequence of the biped robot prototype during a lab test. Experiment results show that the biped robot walks just like a “drunk-man.” But with a step length L that is almost equal to the dimension of the leg mechanism.

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Fig. 16 Snapshots of a walking test by the LARM biped prototype of Fig. 11B.

5.2 LARM hexapod series At LARM a modular anthropomorphic leg has been designed by defining a single link module that can be easily connected with other modules and can have inside all the needed actuators, transmissions and sensors as in ref. [20]. Fig. 17 shows the proposed design for a single link module by using conic gears and timing belt transmissions. The main components of a single link module are: - the body of the module; - a dc motor with reduction gear train; - two conic gears or a timing belt transmission; - two mechanical switches. The link modules can be also properly oriented with respect to the others in order to achieve the required pitch, jaw or roll motions. A link module can be also easily modified in order to drive a wheel in the foot. Dimension of a built prototype leg that is composed by three modules and one wheel in the foot, is high 500 mm and has a cross-section of 60 mm  60 mm, Fig. 17 with a capability of a maximum lift of 155 mm and a step of 310 mm when each joint can rotate +/
90°. The leg module is the basis for the design of hexapode with low-cost user-oriented features that has been developed since 2000, [20].

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Fig. 17 The LARM modular anthropomorphic leg: (A) the mechanical design; (B) a built prototype.

LARM Hexapod family is a series of hybrid legged-wheeled mobile robots that has been designed and built with three version as reported in Fig. 18, [21]. Main characteristics of the LARM Hexapod series are based on the combination of legs and wheels as well as the use of low-cost control architectures to achieve user-friendly solutions. LARM Hexapods have been applied for different inspection operations in non-accessible places. The programming of walking is designed from the analysis of elementary actions to control the operation of the actuators by using signals by suitable switches for the leg mobility [22]. An example of the versatility of the hexapode and its motion planning is shown in Fig. 18 as referring on the obstacle overpassing through a suitable leg motion (Fig. 19).

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Fig. 18 The LARM hexapod robots: (A) version I, (B) version II, (C) version III.

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Fig. 19 Snapshots of locomotion of LARM Hexapod versIIIbis in an obstacle overcoming.

5.3 HeritageBot platform with parallel mechanism legs HeritageBot Platform is a design solution, which integrates a legged mobile robot and a drone module in order to get a robotic platform that has mobility capability both on terrain and aerial areas and the possibility to be equipped with sensors and instrumentation for applications in Cultural Heritage frames, Fig. 20A, as reported in ref. [23]. The HeritageBot Platform has been designed with three modules Fig. 20B: the first module is designed for the control and operation equipment (including batteries and communication hardware) including specific sensors and instrumentation that are needed by the users for specific tasks; the second module is a quadcopter drone system for small flight capability to help avoiding obstacles and to increase payload/stability capacity; the third module is a tripod parallel architecture as locomotion walking system with main features for a very high payload and a wide step range. With such a design, HeritageBot Platform is able to operate in narrow spaces, in presence of obstacles comparable with the HeritageBot platform size while avoiding high pressures or damages on the operation surface. A final prototype of HeritageBot Platform, as version III, has been built at LARM as a proof-of-concept device, Fig. 21, whose overall cost has been limited to less than 10,000 Euros. Commercial components were purchased for the control and operation hardware, batteries, propellers, actuators, and cables and connectors. Main frame of first module and all the remaining structural components have been manufactured via 3D printing The overall size is contained in a box of 50  50  50 cm with a weight of 5.0 kg when equipped, including batteries of 2.0 kg for an operation duration of 2 h while walking at about 250 m/h and flying at less than 1 m height with a tilting capability of 55°. The prototype is equipped with a sonar for obstacle detection, thermal and barometer sensors for environment monitoring, and a telecommunication of 80 m.

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Fig. 20 The conceptual design of the HeritageBot Platform: (A) a scheme design; (B) a modular design.

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Fig. 21 A prototype design of HeritageBot Platform: (A) a CAD design; (B) a built unit.

The leg structure is capable of a large walking step as depending of the stroke of the linear actuators that ensure also a high payload with stiff behavior. As indicated in the modular design, the legged locomotor is fully equipped on board with the necessary control units and sensors by leaving specie for additional equipment as necessary for the application. The flight module is installed on top of the central plate with independent control units and sensors. It is designed for small flight that can increase the locomotion capability in over passing obstacles and can increase the payload capacity of the platform when used as floating unit. Fig. 22 shows an outdoor test of the HeritageBot Platform in a typical motion operation combining walking with a small flight [24]. The combination of walking and small flight makes the system useful in many applications where a single capability cannot be sufficient, beside giving more possibility of motion.

Fig. 22 An outdoor test of the prototype of HeritageBot platform III: (A) outdoor walking operation; (B) small flight operation.

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5.4 Exoskeleton leg mechanism Particular legged systems are the exoskeleton devices that are recently under development for several applications like motion assistance, training exercising, and rehabilitation therapies. In order to develop a low-cost exoskeleton with a fairly simple mechanism structure it can be convenient to simplify and adapt existing solutions with linkage architectures. At LARM linkage solutions have been designed as based on a pantograph and Chebyshev linkage for efficient reproduction of human walking with fairly easily manufactured robust systems and simple operation features [25]. A pantograph is useful for human walking reproduction since it can amplify properly an input motion from the body frame to the foot point. A Chebyshev linkage can be a proper choice for producing an input “human-like” path of ovoid shape with high mechanical efficiency and fairly simple motion control. In Fig. 23 examples of experienced mechanism designs for leg exoskeleton are shown as based on the above combination of a pantograph with a Chebyshev four-far linkage. The solution in Fig. 23A has a high number of links and joints and the ankle joint is missing. Nevertheless, this exoskeleton mechanism shows a good stability during walking. The mechanism design in Fig. 23B has the actuation link (1) on the front and no actuation mechanism on ankle joint, but it cannot permit to place a human subject between exoskeleton legs and the actuator, although the driving link can be placed in the back side. A feasible solution can be identified as in Fig. 23C, with a knee F-joint.

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For the leg exoskeleton solutions in Fig. 23 it is necessary only one actuator that can be placed in joint A on body 0 (the frame). The links can be made adjustable in order to adapt a solution to any human body. It can be observed that the ankle joint for these solutions is neglected due to the impossibility to place a mechanism near the ankle region, as in most of the leg exoskeletons. However, for the ankle joint an equivalent mechanism can be proposed as a cam mechanism, as in the design scheme in Fig. 24 with four links, seven revolute joints, and one cam mechanism. Previous leg mechanisms in Figs. 23 and 24B are based on pantograph and Chebyshev mechanisms, and they have been considered a starting point for developing a solution for a human locomotion assisting system, even in a topology search design procedure. The LARM leg exoskeleton mechanism is presented in Fig. 23C with the additional solution for articulating the motion of ankle joint in coordination with knee and hip motions. The cam mechanism has been placed with a joint at the point E with the possibility to choose any point on the shank link by using a proper cam profile to perform an angular motion as much as similar to the human one. Another LARM leg exoskeleton mechanism has been developed for a specific lower limb design [26]. Most of the currently developed lower extremity exoskeletons are bulky and have limited torque and power making the exoskeletons not fully portable, especially for paralyzed human subjects and their rehabilitation. Therefore, a mechanism solution can be a convenient solution for a lower limb exoskeleton with three degrees-offreedom that can be actuated by electric motors, one rotational servomotor

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for the hip joint and two linear actuators for the leg links. The kinematic design is shown in Fig. 25 where the whole exoskeleton weight is sustained by a support belt that is located at the waist of the user. The mechanism design is actuated by two linear actuators that are installed in parallel inverted slider-crank chains between thigh and shank,

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shank and foot respectively as in the schemes in Fig. 25A and B. The translational motion of the linear actuators provides the rotation of the knee and foot joint. The built prototype in Fig. 25C is a scaled model of a leg exoskeleton, which was assembled by using market components and 3D printing manufacturing. For the actuation of the knee and ankle joints two Firgelli L16 linear actuators were used, with a maximum stroke of 100 mm.

6 Conclusions This chapter presents legged locomotion systems as based on mechanism design by surveying existing solutions and indicating design issues as from the experiences of the authors with a variety of solutions and applications. The large variety of mechanism solutions is illustrated also by examples that refer to a design procedure that has been outlined by considering the characteristics of locomotion and features for user/task-oriented design and operation.

References [1] Oxford Dictionary, Locomotion, Oxford University Press, Oxford, UK, 2019. [2] IFToMM, special issue. Standardization and terminology, Mech. Mach. Theory 38 (2003) 7–10. [3] M. Ceccarelli, E.M. Kececi (Eds.), Designs and Prototypes of Mobile Robots, In: ASME Press Robotics Engineering Book SeriesASME, 2015. [4] J. Liu, M. Tan, X.G. Zhao, Legged robots-an overview, Trans. Inst. Meas. Control. 29 (2) (2007) 185–202. [5] A. Morecki, K.J. Waldron, Human and Machine Locomotion, Springer, New York, 1997. [6] B. Siciliano, O. Khatib (Eds.), Springer Handbook of Robotics, Springer, Cham, 2016. [7] G. Carbone, M. Ceccarelli, Legged robotic systems, in: Cutting Edge Robotics, Intech, Wien, 2005, pp. 553–576. [8] E.M. Kececi, M. Ceccarelli (Eds.), Mobile Robots for Dynamic Environments, In: ASME Press Robotics Engineering Book SeriesASME, 2015 ISBN: 9780791860526. [9] M. Ceccarelli, Fundamentals of Mechanics of Robotic Manipulation, Kluwer/ Springer, Dordrecht, 2004. [10] E. Bautista Paz, M. Ceccarelli, J. Echavarri Otero, J.J. Munoz Sanz, A brief illustrated history of machines and mechanisms, in: Science and Engineering, Book Series on History of Machines and Machine Science, vol. 10, Springer, Dordrecht, 2010. [11] M. Ceccarelli, A historical perspective of robotics toward the future, Fuji Int. J. Robot. Mechatronics 13 (3) (2001) 299–313. [12] M.E. Rosheim, Robot Evolution, Wiley, New York, 1994. [13] I. Kobrinski et al., (Ed.), First CISM-IFToMM ROMANSY (Udine 5-8 September 1973), Springer-Verlag, Wien, 1974. [14] M. Vukobratovic, B. Borovac, Zero-moment point—thirty five years of its life, Int. J. Humanoid Rob. 1 (1) (2004) 157–173.

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[15] S. Hashimoto, A. Takanishi (Eds.), Humanoid Robotics Institute at Waseda University, Waseda University Publishing Office, Tokyo, 2008. [16] C. Lopez-Caju`n, M. Ceccarelli, Mecanismos, Trillas, Mexico City, 2010. [17] J.E. Shigley, G.R. Pennock, J.J. Uicker, Theory of Machines and Mechanisms, McGraw-Hill, New York, 2015. [18] T. Li, M. Ceccarelli, A topology search for a new LARM leg mechanism, in: Proceedings of IFToMM-FeIbIM International Symposium on Mechatronics and Multibody Systems MUSME 2011, Editorial Polytechnic University of Valencia, Valencia, 2011, pp. 77–94. [19] C. Liang, M. Ceccarelli, Y. Takeda, Operation analysis of a Chebyshev-Pantograph leg mechanism for a single DOF biped robot. Front. Mech. Eng. 7 (4) (2012) 357–370, https://doi.org/10.1007/s11465-012-0340. [20] G. Carbone, M. Ceccarelli, A low-cost easy-operation hexapod walking machine, Int. J. Adv. Robot. Syst. 5 (2) (2008) 161–166. [21] F. Tedeschi, G. Carbone, Design issues for hexapod walking robots, Int. J. Robot. 3 (2) (2014) 181–206. [22] G. Carbone, A. Shrot, M. Ceccarelli, Operation strategy for a low-cost easy operation Cassino hexapod, Appl. Bionics Biomech. 4 (4) (2007) 149–156. [23] M. Ceccarelli, D. Cafolla, M. Russo, G. Carbone, HeritageBot platform for service in cultural heritage frames. Int. J. Adv. Robot. Syst. 15 (4) July 1.(2018). https://doi.org/ 10.1177/1729881418790692. [24] M. Ceccarelli, D. Cafolla, M. Russo, G. Carbone, Prototype and testing of HeritageBot platform for service in cultural heritage, in: M. Ceccarelli et al., (Ed.), New Activities for Cultural Heritage, Springer International Publishing AG, 2017, pp. 104–112. [25] C. Copilusi, M. Ceccarelli, G. Carbone, Design and numerical characterization of a new leg exoskeleton for motion assistance, Robotica 33 (2015) 1147–1162. [26] C. Iancu, M. Ceccarelli, E.-C. Lovasz, Design and lab tests of a scaled leg exoskeleton with electric actuators. in: Advances in Service and Industrial Robotics—Proceedings of the 26th International Conference on Robotics in Alpe-Adria-Danube Region RAAD 2017, Springer, 2017, pp. 719–726, https://doi.org/10.1007/978-3-31961276-8_76.

Further reading [27] M. Ceccarelli, Mechanism design for robots, in: Proceedings of the 11th IFToMM International Symposium on Science of Mechanisms and Machines (SYROM’13 Brasov), Springer, Dordrecht, 2013, pp. 1–8. [28] M. Ceccarelli, Leg mechanisms, (Chapter 1).in: M. Ceccarelli, E.F. Kececi (Eds.), Designs and Prototypes of Mobile Robots, ASME Press Robotics Engineering Book SeriesASME, 2015, pp. 1–21.