Abstract
The synthesis of the kinematic chain needs to obtain the information of the kinematic chain accurately and comprehensively. Isomorphism identification is an essential step in kinematic chain synthesis. In this article, a novel isomorphism determination method of planar kinematic chains with multiple joints based on joint–joint matrix description was proposed. First, a joint–joint matrix is presented to describe the kinematic chain, which can uniquely represent the kinematic chain structure. Then links and joints information were extracted from the matrix. And the link code and joint code were introduced to represent the link attributes and joint attributes, respectively. Furthermore, the standardization rules of joint–joint matrix are proposed. Isomorphism of kinematic chain is identified by comparing links, joints, and matrices. And the relationship between the links and the joints corresponding to the isomorphic kinematic chain is determined. Finally, the examples demonstrate that the method is novel and efficient.
Highlights
In 1964, the graph theory was introduced into the study of the topology of kinematic chains
There is a corresponding relationship between the structure diagram and topological graph
J Liu6 suggested a new approach to convert the multiple joints to some parallel simple joints by using a pin-link to adjoin all the links on a multiple joint
Summary
In 1964, the graph theory was introduced into the study of the topology of kinematic chains. The topological description and isomorphism identification of kinematic chains with multiple joint need to be further studied. The element ai, j(i 61⁄4 j) of joint–joint matrix AC1 expresses the connection relationship between joint Ji and joint Jj of the kinematic chain C1 The value of the element a3, 4 is ‘‘4,’’ which indicates that the joint 3 is connected to joint 4, and the serial number of the connected link is 4. In the third row of the joint–joint matrix AC1 , there are the values ‘‘3,’’ ‘‘4,’’ and ‘‘8.’’ It conveys links 3, 4, and 8 connected in multiple joint 3. Ni expresses that the link is i element multiple links
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