Abstract
In this work, a new algorithm is proposed for a unique representation for simple and multiple joint planar kinematic chains (KCs) having any degree of freedom (DOF). This unique representation of KCs enhances the isomorphism detection during the structural synthesis process of KCs. First, a new concept of joint degree is generated for all joints of a given KC based on joint configuration. Then, a unified loop array (ULA) is obtained for each independent loop. Finally, a unified chain matrix (UCM) is established as a unique representation for a KC. Three examples are presented to illustrate the proposed algorithm procedures and to test its validity. The algorithm is applied to get a UCM for planar KCs having 7–10 links. As a result, a complete atlas database is introduced for 7–10-link non-isomorphic KCs with simple or/and multiple joints and their corresponding unified chain matrix.
Highlights
Many techniques are available for isomorphism detection in kinematic chains (KCs) with either simple or multiple joints
Using the unified chain matrix, a complete atlas database is established for planar 7, 8, and 10-links KCs with simple and multiple joints
A new method to represent planar KCs was developed in this paper
Summary
Production and Mechanical Design Department, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt.
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