Research Papers

Global Performance Index System for Kinematic Optimization of Robotic Mechanism

[+] Author and Article Information
Pu Zhang

The State Key Lab of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zhesjtu@gmail.com

Zhenqiang Yao

The State Key Lab of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zqyaosjtu@gmail.com

Zhengchun Du

The State Key Lab of Mechanical System
and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zcdusjtu@gmail.com

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 3, 2013; final manuscript received November 4, 2013; published online December 19, 2013. Assoc. Editor: Chintien Huang.

J. Mech. Des 136(3), 031001 (Dec 19, 2013) (11 pages) Paper No: MD-13-1003; doi: 10.1115/1.4026031 History: Received January 03, 2013; Revised November 04, 2013

Correct evaluation of robot performance has been a problem in the field of robotics. Many scholars have proposed a variety of performance indices, such as manipulability, condition number, and minimum singular value, to describe quantitatively the kinematic performance of a robotic mechanism. However, two questions remain: (1) how to describe the kinematic performance completely for the design of a robotic mechanism, and (2) how to comprehensively describe the global performance distribution characteristics in the workspace. This paper presents a global performance index system for kinematic optimization of a robotic mechanism based on Jacobian matrix, manipulability ellipsoid, and descriptive statistics theory that can comprehensively describe the kinematic performance and the performance distribution characteristics in a robot's workspace. First, the Jacobian matrix, a linear mapping from the joint space to the task space of a robotic mechanism, is analyzed, and the kinematic transmission ability indices and the kinematic transmission accuracy index are determined. Second, four indices, including global average value, global volatility, global skewness, and global kurtosis, are presented to describe the global performance index's distribution in the workspace. Third, the global performance index system is established to evaluate a robot's global kinematic performance based on the above analysis. Finally, a two-degrees of freedom (DOF) robotic mechanism is designed based on the global performance index system as a case, analysis of which shows that the final mechanism has good kinematic performance in the workspace. This demonstrates that the global performance index system proposed in this paper can be useful for the evaluation of the kinematic performance and kinematic optimization of a robotic mechanism.

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Grahic Jump Location
Fig. 1

The manipulability ellipsoid

Grahic Jump Location
Fig. 2

Properties of the manipulability ellipsoid

Grahic Jump Location
Fig. 3

Index distribution in one-dimensional space

Grahic Jump Location
Fig. 4

Kinematic model of the 2-DOF robotic mechanism

Grahic Jump Location
Fig. 5

The dexterity index's distributions with optimal parameters for different target functions

Grahic Jump Location
Fig. 6

The kinematic performance indices' distribution with optimal parameters for target function three



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