This paper addresses the selection of the optimal trajectory and transmission ratio for a servo motor driving a purely inertial load. Both aspects are studied with respect to the required motor torque and are formulated in a dimensionless fashion. Consequently, the results are generally valid and answer the following questions. What is the gain in terms of required motor torque by optimising the trajectory for minimal motor torque given a required smoothness? What is the corresponding optimal trajectory? What is the gain in terms of required motor torque by inserting a mechanism (variable transmission) between the motor and the load? What is this optimised variable transmission ratio? The final example shows how a realistic mechanism can approximate this theoretically optimised variable transmission ratio and, hence, the corresponding reduction in required motor torque.

1.
Angeles, J. and Lo´pez-Caju´n, C, 1991, Optimization of Cam Mechanisms, Kluwer Academic Publishers, Dordrecht-Boston-London.
2.
Asher, U. M., Mattheij, R. M., and Russel, R. D., 1988, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, Prentice Hall, Engle-wood Cliffs, N.J.
3.
Berger, M., Mo¨ckel, J., and Scho¨nherr, J. 1995, “Koppelgetriebe mit Servoantrieb zur exakten Erzeugung flexibler und anpaßbarer ungleichma¨ßiger Bewegungen,” Proceedings to the 9th IFToMM World Congress, Milano, pp. 3033–3037.
4.
Chen, F., 1982, Mechanics and Design of Cam Mechanisms, Pergamon Press, New York.
5.
Childs, B., Scott, M., Daniel, J., Denman, E., and Nelson, P., 1979, Codes for Boundary Value Problems in Ordinary Differential Equations, Springer Verlag, Berlin, Heidelberg, New York.
6.
Dubowsky
S.
, and
Freudenstein
F.
,
1971
, “
Dynamic Analysis of Mechanical Systems with Clearances
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Series B, Vol.
93
, No.
1
, pp.
305
316
.
7.
Greenough, J., Bradshaw, W., Gilmartin, M., Douglas, S., and Rees Jones, J., 1995, “Design of Hybrid Machines,” Proceedings to the 9th IFToMM World Congress, Milano, pp. 2501–2505.
8.
Hendriks, E., ter Heegde, P., and Van Prooijen, T., 1988, “Aspects of a Metal Pushing V-Belt for Automotive Cut Application,” SAE paper 881734, Passenger Car Meeting and Exposition, Dearborn, Michigan.
9.
Lim
K.
, and
Ullman
D.
,
1989
, “
Optimal Design of Traction Drive Continuously Variable Transmissions
,”
ASME Journal of Mechanisms, Transmissions and Automation in Design
, Vol.
111
, pp.
264
259
.
10.
Mabie, H., and Reinholtz, C, 1992, Mechanisms and Dynamics of Machinery, Fourth ed., John Wiley & Sons, New York.
11.
Pasch
K.
, and
Seering
W.
,
1984
, “
On the Drive Systems for High-Performance Machines
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
106
, pp.
102
108
.
12.
Peshkin, M., Colgate, J., and Moore, C., 1996, “Passive Robots and Haptic Displays Based on Nonholonomic Elements,” Proc. IEEE Int. Conf. on Robotics and Automation, Vol. 1, Minneapolis, pp. 551–556.
13.
Sage, A., and White, C, 1977, Optimum Systems Control, Second ed., Prentice Hall, Englewood Cliffs, N.J.
14.
Van Aken, L., 1987, “Robot Motions in Free Space: Task Specification and Trajectory Planning,” Ph.D. thesis, Dept. of Mech. Eng., K. U. Leuven, Leuven.
15.
Van de Straete
H. J.
, and
De Schutter
J.
,
1996
, “
Hybrid Cam Mechanisms
,”
IEEE/ASME Transactions on Mechatronics
, Vol.
1
, No.
4
, pp.
284
289
.
16.
Van de Straete
H. J.
,
De Schutter
J.
,
Degezelle
P.
, and
Belmans
R.
,
1998
, “
Servo Motor Selection Criterion for Mechatronic Applications
,”
IEEE Transactions on Mechatronics
, Vol.
3
, No.
1
, pp.
43
50
.
This content is only available via PDF.
You do not currently have access to this content.