Mechanisms

In the area of kinematics of spatial mechanisms, we have focused our attention on:

calibration of industrial robots, and
singularity analysis of non-redundant mechanisms.

An optimization methodology has been developed in response to potential high costs associated with industrial-robot calibration. The objective of minimizing residual error after calibration is combined with the objective of minimizing the cost of calibration into a multi-criterion non-linear programming problem.

The main difficulty in carrying out such an optimization process is to directly measure the residual error of the robot for every set of variables evaluated by the algorithm. One solution is to use a response-surface methodology can be used to obtain a second-order polynomial response-surface representation of the observed (via experiments or simulations) residual-error data.

In regard to the second area of research, a general theory for the singularity analysis of non-redundant mechanisms has been developed. On the basis of a general velocity equation, derived as a necessary and sufficient condition for the feasibility of the instantaneous motion of a mechanism, a new general definition of singularity is proposed.

The velocity equation explicitly includes the passive-joint velocities in addition to all input and output velocities of the mechanism. A configuration is regarded as singular when either the forward or the inverse kinematics problem does not have a general solution.

Six types of singularities, reflecting different possibilities for the occurrence of indeterminacy of the instantaneous kinematics, were defined.

Platform

Sample Publications

D. Zlatanov, R.G. Fenton, and B. Benhabib, "Identification and Classification of the Singular Configurations of Mechanisms," J. of Mechanism
	and Machine Theory, Vol. 33, No. 6, pp. 743-760, August 1998.
D.S. Zlatanov, R.G. Fenton and B. Benhabib, "Classification and Interpretation of the Singularities of Redundant Mechanisms," ASME, 24th
	Annual Design Automation Conference, Atlanta, Georgia, CD Proceedings, Paper #DETC98/MECH-5896, September 1998.
D. Zlatanov, R.G. Fenton, and B. Benhabib, "A Unifying Framework for Classification and Interpretation of Mechanism Singularities," ASME, J.
	of Mechanical Design, Vol. 117, No. 4, pp. 566-572, December 1995.
S. Kaizerman, B. Benhabib, R.G. Fenton, and G. Zak, "A Sensitivity Analysis Based Method for Robot Calibration," ASME, J. of Mechanical
	Design, Vol. 116, No. 2, pp. 607-613, June 1994.
G. Zak, R.G. Fenton, and B. Benhabib, "Determination of the Optimum Cost-Residual Error Trade-off in Robot Calibration," ASME, J. of
	Mechanical Design, Vol. 116, No. 1, pp. 28-35, March 1994.