Robotics and Autonomous Systems 53 (2005) 153–163 A kinematics performance index based on the rate of change of a standard isotropy condition for robot design optimization Ren´ e V. Mayorga ∗ , Johnatan Carrera, Maria M. Oritz Faculty of Engineering, University of Regina, Regina, Saskatchewan, Canada S4S 0A2 Received 8 December 2002; received in revised form 20 July 2004; accepted 30 September 2005 Abstract In this article a simple performance index for robot manipulator kinematic design optimization and/or best posture determi- nation is presented. This index is derived from a homogenized isotropy condition of a properly weighted Jacobian matrix. Here it is shown that it is relatively easy to determine a joint configuration neighborhood where a homogenized isotropy condition changes the least. Here the proposed index is applied to the kinematic design optimization and best posture determination of a redundant manipulator, and compared with the results obtained from using other performance indices. From the results obtained it can be observed that the proposed index compares favorably with other performance indices. © 2005 Elsevier B.V. All rights reserved. Keywords: Dexterity; Kinematic design; Isotropic condition; Path planning; Performance criteria; Singularities; Task planning 1. Introduction In the past decade, several studies on robot (redun- dant) manipulators design have been performed for the kinematic evaluation of some designs [4,6], and [21]. The main objective of these studies was to develop a dexterity measure (with respect to singularities proxim- ity/remoteness) by establishing a performance index: derived from the singular value decomposition of the Jacobian matrix [4,6]; or from the square root of the de- terminant of the Jacobian matrix by its transpose [21]. ∗ Corresponding author. Tel.: +1 306 585 4726; fax: +1 306 585 4855. Although these approaches for some particular cases can provide local performance (on neighbor or distant singularities regions) information; however, they are neither suitable for a simple global design analysis nor useful for the comparison of different designs. This also holds true for the approach based on an isotropy cri- terion presented in [1]; although this approach can be used to determine best postures and locally optimized designs of general manipulators. Moreover, in the gen- eral case the approaches cannot be utilized to measure manipulator performance invariant to frame reference selection and/or scaling [2,8]. In [12] similar concepts as in [14,16], and [17], were followed to develop a simple kinematic criterion for 0921-8890/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.robot.2005.09.010