- Email: [email protected]
A study on a hybrid actuator
Mechanism and Machine Theory 35 (2000) 1141±1149
www.elsevier.com/locate/mechmt
A study on a hybrid actuator Ali Kirec° ci*, L. Canan Dulger Mechanical Engineering Department, Gaziantep University, 27310 Gaziantep, Turkey Received 17 August 1998; accepted 19 May 1999
Abstract Classically, constant speed motors drive some mechanical transmissions such as gears, cams and linkages in order to produce non-uniform motion in machines. Such machines may allow a limited ¯exibility, by changing dimensions of the components. To answer the need for ¯exibility constant speed motors are replaced by servomotors. Besides other disadvantages, the cost of this solution is often very high especially for large capacity machines. Hybrid machines, which are a combination of two types of motors and mechanisms, have ¯exibility at a reduced cost. A new hybrid actuator is proposed in the study presented here. 7 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction The main idea behind hybrid systems is to combine the motion of a large constant speed motor with a small servomotor via a two degree of freedom (DOF) mechanism, where, the constant speed motor provides the main torque and motion requirements, while the servomotor contributes to modulations on this motion. Hybrid systems may be classi®ed as hybrid actuator and hybrid mechanism. An intelligent box having two inputs and one output is considered as the hybrid actuator as shown in Fig. 1. The box is driven by a servomotor and a constant speed motor and provides a programmable output which may be coupled to a mechanism or a load. However, a hybrid mechanism is one that has at least two degrees of freedom. That means, the mechanism has two input links which are coupled to a servomotor and a constant speed motor. * Corresponding author. Tel.: +342-360-1200; fax: +342-360-1100. E-mail address: [email protected] (A. Kirec° ci). 0094-114X/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 9 4 - 1 1 4 X ( 9 9 ) 0 0 0 5 9 - 2
1142
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
The idea of hybrid machine was initially investigated by Tokuz and Jones [1]. In their study, the motion of a constant speed motor and a servomotor were combined by a dierential gearbox to drive a slider-crank mechanism. They have pointed out some important conclusions with this type of hybrid arrangement. For example, they have shown that considerable amount of power was saved for the servomotor from the arrangement of some motion types. However, for dwell type of motions of the arrangement, the servomotor is required to produce power as much as the power of the constant speed motor. Since, it is obvious that to obtain a dwell motion the servomotor has to oppose the motion of the constant speed motor. A two DOF mechanism (seven-bar linkage) is replaced instead of a dierential gearbox to overcome the diculties producing dwell motion in the study of Greenough and Bradshaw [2]. The mechanism is ®xed to the frame by three revolute joints. One of the joints is actuated by a constant speed motor, while the second one by a servomotor. The third joint is considered the output of the hybrid mechanism. Results show that the power requirement of the servomotor is reduced, although not to a predicted degree. However, the research continues for the minimisation of the servomotor by optimising link lengths of the mechanism. Kirecci and Tokuz have proposed another hybrid arrangement which is capable of doing any motion in the X±Y plane [3]. The main motion in the X-direction is produced by a slidercrank mechanism that has an adjustable crank length. A power screw mechanism, carried by the slider and actuated by a servomotor, is used to produce modulations in the motion of the slider to achieve the desired motion in this direction. The motion in the Y-direction is produced by a direct servomotor driven power screw mechanism. Some particular applications of the hybrid machines have already been seen in industry. Cut to length machine, web printing machine and injection moulding machine are the examples of such types of machines. Cut to length machine consists of a pair of high inertia cylinders, each of which is driven by a servomotor. Each cylinder has a blade attached to it. A precise sharing action can only be produced when the velocity of blades meets the velocity of the material that will be cut. The same action is also obtained by introducing a hybrid actuator in which the constant speed motor and servomotor are combined together with a dierential gearbox. The output motion of the hybrid actuator was so arranged that the speed of the cylinders exactly
Fig. 1. Hybrid actuator.
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
1143
match the speed of the web. In this particular application, the peak power of the servomotor has been reduced by approximately 70% [4]. Web printing machines may be another potential application area of hybrid actuators. The working principles of this machine are quite similar to that of cut to length machine, such that, instead of blades stereotypes may be attached to the high inertia cylinders, where the number of cylinders is dependent on the number of colours used for printing. To obtain a high quality printing, the speed of the cylinders must match the speed of the web. Injection moulding machine is another example in which hybrid mechanism was already used. In this machine, a variable frequency motor incorporates with an AC motor to power electric screw drives and hydraulic pumps. This arrangement reduces machine energy consumption by as much as 60%, compared to traditional hydraulic machine [5].
2. Design of hybrid actuator The basic requirement for a hybrid actuator is to provide a programmable output combining the motion of a constant velocity motor with the motion of a servo motor by means of a two DOF mechanism as shown in Fig. 1. The most suitable mechanism is a dierential gearbox, however, some important drawbacks related with the use of dierential gearbox for the hybrid actuator, is already mentioned. On the other hand, there may be several linkage mechanisms which may be used for this purpose. Some of them will be examined by a systematic way in this study. By means of number synthesis, link type, link number and joint number can be determined, in terms of DOF, and total link number of a mechanism [6]. In this study, link combinations for two DOF, upto seven links, to hexagonal order and using only full revolute joints will be examined. Initially, kinematic chains will be produced for each combination of links, then using these chains, mechanisms will be created by inversion method to examine all potential candidate mechanisms that may be used for a hybrid actuator. The general DOF equation (Grubler's equation) is, DOF 3 L ÿ 1 ÿ 2J1 ÿ J2
1
where, J1 is the number of full joints, J2 the number of half joints and L the number of total links. The Grubler's equation can be written as follows, when the half joint is omitted, DOF 3 L ÿ 1 ÿ 2J
2
The total number of links in any mechanism will be, LBTQPH
3
where, B is the number of binary links, T the number of ternary links, Q the number of quaternary links, P the number of pentagonal links, H the number of hexagonal links. And the number of joints is,
1144
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
3 DOF J L ÿ 1 ÿ 2 2
4
To determine link combinations, Eqs. (1) and (2) are joined. DOF 3 L 2 B T Q P H ÿ 2B 3T 4Q 5P 6H and L ÿ DOF ÿ 3 T 2Q 3P 4H
5
All compatible link combinations are determined by using Eqs. (3) and (5) systematically, as shown in Table 1. The ®rst column of the table shows the total number of links and the other columns show binary, ternary, quaternary, pentagonal and hexagonal links in each combination. In order to produce mechanisms, kinematic chains are created for each case and then using these kinematic chains, mechanisms are generated for each kinematic chain as shown in Fig. 2. The ®rst row of Table 1 shows that a two DOF mechanism can be produced using ®ve binary links. This is simply a ®ve-bar mechanisms. However, this mechanism does not serve our purpose, because the mechanisms that will be used for hybrid actuator must be ®xed to the ground by means of three revolute joints; two of them for inputs and one for the output. Therefore, the mechanisms produced by grounding a ternary or higher order link to the frame may be the only suitable mechanism. When the total number of links is seven, two dierent cases are possible as shown in the second and third row of Table 1. All possible kinematic chains, using ®ve binary and two ternary links, are given in Fig. 2a±e. For each kinematic chain, several mechanisms can be produced by grounding dierent links of that kinematic chain. Some of them are given in Fig. 2f±p. It seems that two dierent desirable mechanisms can be produced from each kinematic chain, because each kinematic chain has two ternary links. However, since they are symmetric both alternatives will give the same mechanism, therefore, only one mechanism can be produced from each kinematic chain as shown in Fig. 2f±j. Furthermore, the motion of each axis of the mechanism must not be completely dependent on the motion of the other one axis, but on the combination of other two axes. Therefore, the mechanisms shown in Fig. 2h±j can also be eliminated. Consequently, Fig. 2f and g are the only suitable mechanisms. However, when they are examined carefully, it will be seen that those mechanisms are the same. As a result, there is only one mechanism that may be used for hybrid actuator for the case given in the second row of Table 1 (Fig. 2f), if all the joints are revolute joints. This Table 1 All possible link combinations for two DOF mechanism up to seven links Total number of links
B
T
Q
P
H
5 7 7
5 5 6
± 2 ±
± ± 1
± ± ±
± ± ±
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
1145
Fig. 2. Kinematic chains and mechanism.
mechanism is the same as initially designed by Svobada [7], and it is already used for hybrid actuator purposes in the study of Greenough and Bradshow. Using the next alternative given in the third row of Table 1, we may produce only following kinematic chains shown in Fig. 3. Obviously, these kinematic chains may not be used for a hybrid actuator purpose. Furthermore, many other candidate mechanisms may be produced just by changing some
Fig. 3. Seven link kinematic chains.
1146
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
Fig. 4. Producing dierent mechanisms by changing joint types and shrinking links.
joint types and partially shrinking some higher order links. As an example, the mechanism used in this study is obtained with the modi®cation of Fig. 2j. The link indicated by 4 is shrunk to be a binary link, and revolute joint (E ) is replaced by a prismatic joint as shown in Fig. 4. 3. The experimental arrangement The arrangement comprised of a planar two degree of freedom, seven-link mechanism is shown schematically in Fig. 5, where, the grounded axes A is driven by a servo motor instead of a C.S. motor to obtain accurate current values experimentally. The other axis indicated by E is driven by the second servomotor. The third axis G is used for the output of the mechanism that is directly connected to the load.
Fig. 5. Experimental arrangement.
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
1147
All system control was carried out at the servo axes level with inverse kinematics being used to calculate joint angles required for a speci®ed motion of the load. The output motions are designed to pass through a number of speci®ed data points including position, velocity and acceleration values using motion design software MOTDES [8]. Proportional and derivative (PD) control is applied in order to reduce the tracing errors of the system [9]. A low-pass digital ®lter is used in order to eliminate noise eects from the data taken by the analogue± digital converter [10].
4. Implementation Several example trajectories have been implemented to the system and one of them is given here as an example. The desired and the actual motions of axes are given in Fig. 6. The output motions of the arrangement are given in Fig. 7, where the solid line shows the output when the axis E is not activated. The dashed line shows the modulations on the output of the system due to the eect of second axis. Power requirements of both the axes are shown in Fig. 8. In order to obtain power curves, the current values of each axis are taken by an A/D converter, then power values are calculated using known torque constants and angular velocities. The peak power requirement of servomotor is 3.5 times less than the peak power of C.S. motor. If we consider that all the powers are used to drive the load (this assumption may be true for large capacity machines), the peak power (size of the servomotor) is reduced by at least 3 times that of a normal application.
Fig. 6. Command and response curves.
1148
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
Fig. 7. Output motions.
5. Conclusions The hybrid actuator has certainly some advantages and drawbacks which may be summarised as follows; . A hybrid actuator may save considerable amount of energy when the mass moment of
Fig. 8. Power curves.
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
1149
inertia of the hybrid actuator is reduced to the required degree, because, an important amount of energy will be converted into heat energy in direct-drive servomotor applications. . The initial cost of the actuator depends on the power requirement of the machine. The need for higher power requirement will reduce the relative cost of the hybrid actuator when compared with the direct servo drive systems, because the cost of the servomotor is directly proportional to its size. . The hybrid arrangement combines the motion of the two motors, which may increase the control problem of the system. Furthermore, the power saving ratio depends on the required modulations performed by the servomotor. Obviously, higher modulations will reduce this ratio. Also another factor is that some hybrid actuator may perform better for some motions. For example, the hybrid arrangement designed by Tokuz and Jones [1] may not save energy if a dwell section is required in the output motion of the arrangement. However, the power saving ratio reaches its maximum value for dwell sections in the arrangement presented in this study.
Acknowledgements This project was sponsored by the University of Gaziantep Research Fund. We gratefully acknowledge the Rector of the Gaziantep University and the Research stas. References [1] L.C. Tokuz, J.R. Jones, Hybrid Machine Modelling and Control, Ph.D. Thesis, Liverpool Polytechnic (1992). [2] J.D. Greenough, W.K. Bradshaw, M.J. Gilmartin, S.S. Douglas, J.R. Jones, Design of hybrid machines, Proceedings of the Ninth World Congress for the Theory of Machines and Mechanism 4 (1995) 2501±2505. [3] A. Kirecci, L.C. DuÈlger, Hibrid ManipulatoÈruÈn Modelleme ve Similasyonu, 7. Ulusal Makina Teorisi ve Sempozyumu, Yildiz Teknik UÈniversitesi, Istanbul, 1995. [4] A.M. Conner, The Synthesis of Hybrid Mechanism using Genetic Algorithm, Ph.D. Thesis, Liverpool Polytechnic (1996). [5] Rockwell Automation, Press Release, (www.ab.com./events/pressrel/9706/97061d.html). [6] R.L. Norton, Design of Machinery. An Introduction to the Synthesis and Analysis of Mechanism and Machines, McGraw-Hill, New York, 1992. [7] A. Svobada, Computing Mechanism and Linkages, McGraw-Hill, New York, 1948. [8] A. Kirecci, M. Gilmartin, Trajectory planning for robotic manipulators, in: Sixth International Machine Design and Production Conference, METU, Turkey, 1994. [9] K. Ogata, Modern Control Engineering, Prentice-Hall, Englewood Clis, NJ, 1990. [10] C.S. Williams, Desining Digital Filters, Prentice-Hall, Englewood Clis, NJ, 1986.
www.elsevier.com/locate/mechmt
A study on a hybrid actuator Ali Kirec° ci*, L. Canan Dulger Mechanical Engineering Department, Gaziantep University, 27310 Gaziantep, Turkey Received 17 August 1998; accepted 19 May 1999
Abstract Classically, constant speed motors drive some mechanical transmissions such as gears, cams and linkages in order to produce non-uniform motion in machines. Such machines may allow a limited ¯exibility, by changing dimensions of the components. To answer the need for ¯exibility constant speed motors are replaced by servomotors. Besides other disadvantages, the cost of this solution is often very high especially for large capacity machines. Hybrid machines, which are a combination of two types of motors and mechanisms, have ¯exibility at a reduced cost. A new hybrid actuator is proposed in the study presented here. 7 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction The main idea behind hybrid systems is to combine the motion of a large constant speed motor with a small servomotor via a two degree of freedom (DOF) mechanism, where, the constant speed motor provides the main torque and motion requirements, while the servomotor contributes to modulations on this motion. Hybrid systems may be classi®ed as hybrid actuator and hybrid mechanism. An intelligent box having two inputs and one output is considered as the hybrid actuator as shown in Fig. 1. The box is driven by a servomotor and a constant speed motor and provides a programmable output which may be coupled to a mechanism or a load. However, a hybrid mechanism is one that has at least two degrees of freedom. That means, the mechanism has two input links which are coupled to a servomotor and a constant speed motor. * Corresponding author. Tel.: +342-360-1200; fax: +342-360-1100. E-mail address: [email protected] (A. Kirec° ci). 0094-114X/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 9 4 - 1 1 4 X ( 9 9 ) 0 0 0 5 9 - 2
1142
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
The idea of hybrid machine was initially investigated by Tokuz and Jones [1]. In their study, the motion of a constant speed motor and a servomotor were combined by a dierential gearbox to drive a slider-crank mechanism. They have pointed out some important conclusions with this type of hybrid arrangement. For example, they have shown that considerable amount of power was saved for the servomotor from the arrangement of some motion types. However, for dwell type of motions of the arrangement, the servomotor is required to produce power as much as the power of the constant speed motor. Since, it is obvious that to obtain a dwell motion the servomotor has to oppose the motion of the constant speed motor. A two DOF mechanism (seven-bar linkage) is replaced instead of a dierential gearbox to overcome the diculties producing dwell motion in the study of Greenough and Bradshaw [2]. The mechanism is ®xed to the frame by three revolute joints. One of the joints is actuated by a constant speed motor, while the second one by a servomotor. The third joint is considered the output of the hybrid mechanism. Results show that the power requirement of the servomotor is reduced, although not to a predicted degree. However, the research continues for the minimisation of the servomotor by optimising link lengths of the mechanism. Kirecci and Tokuz have proposed another hybrid arrangement which is capable of doing any motion in the X±Y plane [3]. The main motion in the X-direction is produced by a slidercrank mechanism that has an adjustable crank length. A power screw mechanism, carried by the slider and actuated by a servomotor, is used to produce modulations in the motion of the slider to achieve the desired motion in this direction. The motion in the Y-direction is produced by a direct servomotor driven power screw mechanism. Some particular applications of the hybrid machines have already been seen in industry. Cut to length machine, web printing machine and injection moulding machine are the examples of such types of machines. Cut to length machine consists of a pair of high inertia cylinders, each of which is driven by a servomotor. Each cylinder has a blade attached to it. A precise sharing action can only be produced when the velocity of blades meets the velocity of the material that will be cut. The same action is also obtained by introducing a hybrid actuator in which the constant speed motor and servomotor are combined together with a dierential gearbox. The output motion of the hybrid actuator was so arranged that the speed of the cylinders exactly
Fig. 1. Hybrid actuator.
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
1143
match the speed of the web. In this particular application, the peak power of the servomotor has been reduced by approximately 70% [4]. Web printing machines may be another potential application area of hybrid actuators. The working principles of this machine are quite similar to that of cut to length machine, such that, instead of blades stereotypes may be attached to the high inertia cylinders, where the number of cylinders is dependent on the number of colours used for printing. To obtain a high quality printing, the speed of the cylinders must match the speed of the web. Injection moulding machine is another example in which hybrid mechanism was already used. In this machine, a variable frequency motor incorporates with an AC motor to power electric screw drives and hydraulic pumps. This arrangement reduces machine energy consumption by as much as 60%, compared to traditional hydraulic machine [5].
2. Design of hybrid actuator The basic requirement for a hybrid actuator is to provide a programmable output combining the motion of a constant velocity motor with the motion of a servo motor by means of a two DOF mechanism as shown in Fig. 1. The most suitable mechanism is a dierential gearbox, however, some important drawbacks related with the use of dierential gearbox for the hybrid actuator, is already mentioned. On the other hand, there may be several linkage mechanisms which may be used for this purpose. Some of them will be examined by a systematic way in this study. By means of number synthesis, link type, link number and joint number can be determined, in terms of DOF, and total link number of a mechanism [6]. In this study, link combinations for two DOF, upto seven links, to hexagonal order and using only full revolute joints will be examined. Initially, kinematic chains will be produced for each combination of links, then using these chains, mechanisms will be created by inversion method to examine all potential candidate mechanisms that may be used for a hybrid actuator. The general DOF equation (Grubler's equation) is, DOF 3 L ÿ 1 ÿ 2J1 ÿ J2
1
where, J1 is the number of full joints, J2 the number of half joints and L the number of total links. The Grubler's equation can be written as follows, when the half joint is omitted, DOF 3 L ÿ 1 ÿ 2J
2
The total number of links in any mechanism will be, LBTQPH
3
where, B is the number of binary links, T the number of ternary links, Q the number of quaternary links, P the number of pentagonal links, H the number of hexagonal links. And the number of joints is,
1144
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
3 DOF J L ÿ 1 ÿ 2 2
4
To determine link combinations, Eqs. (1) and (2) are joined. DOF 3 L 2 B T Q P H ÿ 2B 3T 4Q 5P 6H and L ÿ DOF ÿ 3 T 2Q 3P 4H
5
All compatible link combinations are determined by using Eqs. (3) and (5) systematically, as shown in Table 1. The ®rst column of the table shows the total number of links and the other columns show binary, ternary, quaternary, pentagonal and hexagonal links in each combination. In order to produce mechanisms, kinematic chains are created for each case and then using these kinematic chains, mechanisms are generated for each kinematic chain as shown in Fig. 2. The ®rst row of Table 1 shows that a two DOF mechanism can be produced using ®ve binary links. This is simply a ®ve-bar mechanisms. However, this mechanism does not serve our purpose, because the mechanisms that will be used for hybrid actuator must be ®xed to the ground by means of three revolute joints; two of them for inputs and one for the output. Therefore, the mechanisms produced by grounding a ternary or higher order link to the frame may be the only suitable mechanism. When the total number of links is seven, two dierent cases are possible as shown in the second and third row of Table 1. All possible kinematic chains, using ®ve binary and two ternary links, are given in Fig. 2a±e. For each kinematic chain, several mechanisms can be produced by grounding dierent links of that kinematic chain. Some of them are given in Fig. 2f±p. It seems that two dierent desirable mechanisms can be produced from each kinematic chain, because each kinematic chain has two ternary links. However, since they are symmetric both alternatives will give the same mechanism, therefore, only one mechanism can be produced from each kinematic chain as shown in Fig. 2f±j. Furthermore, the motion of each axis of the mechanism must not be completely dependent on the motion of the other one axis, but on the combination of other two axes. Therefore, the mechanisms shown in Fig. 2h±j can also be eliminated. Consequently, Fig. 2f and g are the only suitable mechanisms. However, when they are examined carefully, it will be seen that those mechanisms are the same. As a result, there is only one mechanism that may be used for hybrid actuator for the case given in the second row of Table 1 (Fig. 2f), if all the joints are revolute joints. This Table 1 All possible link combinations for two DOF mechanism up to seven links Total number of links
B
T
Q
P
H
5 7 7
5 5 6
± 2 ±
± ± 1
± ± ±
± ± ±
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
1145
Fig. 2. Kinematic chains and mechanism.
mechanism is the same as initially designed by Svobada [7], and it is already used for hybrid actuator purposes in the study of Greenough and Bradshow. Using the next alternative given in the third row of Table 1, we may produce only following kinematic chains shown in Fig. 3. Obviously, these kinematic chains may not be used for a hybrid actuator purpose. Furthermore, many other candidate mechanisms may be produced just by changing some
Fig. 3. Seven link kinematic chains.
1146
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
Fig. 4. Producing dierent mechanisms by changing joint types and shrinking links.
joint types and partially shrinking some higher order links. As an example, the mechanism used in this study is obtained with the modi®cation of Fig. 2j. The link indicated by 4 is shrunk to be a binary link, and revolute joint (E ) is replaced by a prismatic joint as shown in Fig. 4. 3. The experimental arrangement The arrangement comprised of a planar two degree of freedom, seven-link mechanism is shown schematically in Fig. 5, where, the grounded axes A is driven by a servo motor instead of a C.S. motor to obtain accurate current values experimentally. The other axis indicated by E is driven by the second servomotor. The third axis G is used for the output of the mechanism that is directly connected to the load.
Fig. 5. Experimental arrangement.
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
1147
All system control was carried out at the servo axes level with inverse kinematics being used to calculate joint angles required for a speci®ed motion of the load. The output motions are designed to pass through a number of speci®ed data points including position, velocity and acceleration values using motion design software MOTDES [8]. Proportional and derivative (PD) control is applied in order to reduce the tracing errors of the system [9]. A low-pass digital ®lter is used in order to eliminate noise eects from the data taken by the analogue± digital converter [10].
4. Implementation Several example trajectories have been implemented to the system and one of them is given here as an example. The desired and the actual motions of axes are given in Fig. 6. The output motions of the arrangement are given in Fig. 7, where the solid line shows the output when the axis E is not activated. The dashed line shows the modulations on the output of the system due to the eect of second axis. Power requirements of both the axes are shown in Fig. 8. In order to obtain power curves, the current values of each axis are taken by an A/D converter, then power values are calculated using known torque constants and angular velocities. The peak power requirement of servomotor is 3.5 times less than the peak power of C.S. motor. If we consider that all the powers are used to drive the load (this assumption may be true for large capacity machines), the peak power (size of the servomotor) is reduced by at least 3 times that of a normal application.
Fig. 6. Command and response curves.
1148
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
Fig. 7. Output motions.
5. Conclusions The hybrid actuator has certainly some advantages and drawbacks which may be summarised as follows; . A hybrid actuator may save considerable amount of energy when the mass moment of
Fig. 8. Power curves.
A. Kirec° ci, L.C. Dulger / Mechanism and Machine Theory 35 (2000) 1141±1149
1149
inertia of the hybrid actuator is reduced to the required degree, because, an important amount of energy will be converted into heat energy in direct-drive servomotor applications. . The initial cost of the actuator depends on the power requirement of the machine. The need for higher power requirement will reduce the relative cost of the hybrid actuator when compared with the direct servo drive systems, because the cost of the servomotor is directly proportional to its size. . The hybrid arrangement combines the motion of the two motors, which may increase the control problem of the system. Furthermore, the power saving ratio depends on the required modulations performed by the servomotor. Obviously, higher modulations will reduce this ratio. Also another factor is that some hybrid actuator may perform better for some motions. For example, the hybrid arrangement designed by Tokuz and Jones [1] may not save energy if a dwell section is required in the output motion of the arrangement. However, the power saving ratio reaches its maximum value for dwell sections in the arrangement presented in this study.
Acknowledgements This project was sponsored by the University of Gaziantep Research Fund. We gratefully acknowledge the Rector of the Gaziantep University and the Research stas. References [1] L.C. Tokuz, J.R. Jones, Hybrid Machine Modelling and Control, Ph.D. Thesis, Liverpool Polytechnic (1992). [2] J.D. Greenough, W.K. Bradshaw, M.J. Gilmartin, S.S. Douglas, J.R. Jones, Design of hybrid machines, Proceedings of the Ninth World Congress for the Theory of Machines and Mechanism 4 (1995) 2501±2505. [3] A. Kirecci, L.C. DuÈlger, Hibrid ManipulatoÈruÈn Modelleme ve Similasyonu, 7. Ulusal Makina Teorisi ve Sempozyumu, Yildiz Teknik UÈniversitesi, Istanbul, 1995. [4] A.M. Conner, The Synthesis of Hybrid Mechanism using Genetic Algorithm, Ph.D. Thesis, Liverpool Polytechnic (1996). [5] Rockwell Automation, Press Release, (www.ab.com./events/pressrel/9706/97061d.html). [6] R.L. Norton, Design of Machinery. An Introduction to the Synthesis and Analysis of Mechanism and Machines, McGraw-Hill, New York, 1992. [7] A. Svobada, Computing Mechanism and Linkages, McGraw-Hill, New York, 1948. [8] A. Kirecci, M. Gilmartin, Trajectory planning for robotic manipulators, in: Sixth International Machine Design and Production Conference, METU, Turkey, 1994. [9] K. Ogata, Modern Control Engineering, Prentice-Hall, Englewood Clis, NJ, 1990. [10] C.S. Williams, Desining Digital Filters, Prentice-Hall, Englewood Clis, NJ, 1986.