Dynamic Performance Evaluation of a Parallel Manipulator with Non Axial Symmetrical Characteristics by Computing the Respective Actuating Joint Capability

Dynamic Performance Evaluation of a Parallel Manipulator with Non Axial Symmetrical Characteristics by Computing the Respective Actuating Joint Capability

Yongjie Zhao (Department of Mechatronics Engineering, Shantou University, & Shantou Institute for Light Industrial Equipment Research, Shantou City, Guangdong, China) and Yanling Tian (School of Mechanical Engineering, Tianjin University, Tianjin, Tianjin, China)
Copyright: © 2012 |Pages: 14
DOI: 10.4018/ijimr.2012100101
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Abstract

Unlike the traditional Gough-Stewart platform with axial symmetrical structure, a parallel manipulator consists of non axial symmetrical structure has non axial symmetrical characteristic in the whole reachable workspace. This paper presents the joint capability evaluation of a parallel manipulator with non axial symmetrical characteristics. A series of velocity, torque and power indices are presented. The torque indices combining the acceleration, velocity, and gravity components of the dynamic model are used to evaluate the respective joint torque capability. The power indices corresponding to the torque indices are also adopted to evaluate the respective joint power capability. The joint capability evaluation of the parallel manipulator is carried out through computational analysis and simulation with the velocity, torque and power indices. It is shown that the respective actuating joint capabilities of the parallel manipulator are not uniform due to the non axial symmetrical structure. Thus the performance evaluation of this type of parallel manipulator must be performed by analyzing the respective joint capability. By means of these indices with obvious physical meanings, it is possible to control the respective joint capability of the parallel manipulator. The indices are general and can be used for the other types of parallel manipulators.
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Introduction

Seismic simulator is one of the most important equipment in the earthquake resistance testing. Due to the requirement of the large and variable load capability, these equipments are usually developed with parallel manipulators (Zhao, 2009). Unlike the traditional Gough-Stewart platform with axial symmetrical structure, this type of parallel manipulator consists of non axial symmetrical structure. It has non axial symmetrical characteristic in the whole reachable workspace and the capability of each actuating joint is not uniform any more for this type parallel manipulator. So the respective joint capability should be evaluated when investigating the dynamic performance of the parallel manipulator. In fact, the dynamic models of parallel manipulators are strongly non-linear equations, which make it become difficult to predict the dynamic performance of the manipulator. However, the dynamic performance of parallel manipulator should be considered for the dynamic optimum design, advanced control, prototype building and application (Zhao, 2011; Alici, 2006; Tian, 2010, 2011).

Performance evaluation for parallel manipulator is still an important area of study (Merlet, 2006; Zhao, 2009). Many investigations have been conducted on the kinematic performance evaluation. There are two basic kinematic criteria, (i) the conditioning indices (Gosselin & Angeles, 1988, 1989, 1991; Lipkin & Duffy, 1988; Doty, 1993, 1995; Gosselin, 1990; Pond, 2006; Altuzarra, 2006; Kim, 2003) and (ii) the manipulability measures (Yoshikawa, 1985, 1991; Hong, 2000). According to the matrix theory, the condition number is the ratio of the maximum singular value to the minimum singular value of the matrix and the manipulability can be represented by the continued multiplication of all the singular values. The kinematic manipulability is interpreted as a capability of executing a specific task in a given configuration (Yoshikawa, 1985). Yoshikawa defined the manipulability measure as a generalized determinant of the Jacobian matrix and divided the total manipulability measure into translational and rotational manipulability measure (Yoshikawa, 1991).

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