This article addresses the problem of designing a robotic mechanism su
ch that its end-effector frame comes closest to reaching a set of desi
red goal frames. We formulate this as an optimization problem, in whic
h the kinematic parameters are selected to minimize the total distance
between the end-effector frame and each goal frame. The objective fun
ction is defined in terms of a class of distance metrics on the rigid
body motions that are invariant with respect to choice of fixed refere
nce frame. A main contribution of this article is an explicit expressi
on for the gradient of this objective function with respect to the kin
ematic parameters. With this analytic gradient, efficient optimization
algorithms can now be developed for the design of general spatial mec
hanisms. Our design methodology is illustrated with an example involvi
ng the base positioning of two cooperating robots. (C) 1995 John Wiley
& Sons, Inc.