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Technical Brief

# Solution Region Synthesis Methodology of Spatial 5-SS Linkages for Six Given Positions

[+] Author and Article Information
Jianyou Han

School of Mechanical Engineering,
University of Science and Technology, Beijing,
Beijing 100083, China
e-mail: jyhan@ustb.edu.cn

Guangzhen Cui

School of Mechanical Engineering,
University of Science and Technology, Beijing
Beijing 100083, China
e-mail: c_u_i_guangzhen@163.com

1Corresponding author.

Manuscript received August 8, 2016; final manuscript received February 24, 2017; published online May 2, 2017. Assoc. Editor: Shaoping Bai.

J. Mechanisms Robotics 9(4), 044501 (May 02, 2017) (5 pages) Paper No: JMR-16-1229; doi: 10.1115/1.4036219 History: Received August 08, 2016; Revised February 24, 2017

## Abstract

This paper presents a solution region synthesis methodology to perform the dimensional synthesis of spatial 5-spherical–spherical (SS) linkages for six specified positions of the end-effector. Dimensional synthesis equations for an SS link are formulated. After solving the synthesis equations, the curves of moving and fixed joints can be obtained, and they are called moving and fixed solution curves, respectively. Each point on the curves represents an SS link. Considering the limited range of joints at the first position, we can obtain the feasible solution curves. The link length curves can be obtained based on the feasible solution curves. We determine three SS links by selecting three points meeting the requirements on link length curves. Then, the solution region is built by sorting and adding feasible solution curves and projecting the feasible solution curves on the line. The feasible solution region can be obtained by eliminating defective linkages and linkages that fail to meet the other requirements from the solution region. The validity of the formulas and applicability of the proposed approach is illustrated by example.

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## Figures

Fig. 3

Six specified positions

Fig. 2

Fig. 1

Fig. 4

(a) Moving solution curves and (b) moving solution curves in the X–Y plane

Fig. 5

Fig. 6

(a) Solution region, (b) feasible solution region, and (c) feasible solution region meeting link length requirement

Fig. 7

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