Topology of Kinematic Chains with Loops and Orientation of Joints Axes

Abstract

A topological characteristics matrix with information of loops, types of links and joints, and orientations of joints is proposed. Loops are formed according to the kinds of links (binary or multi-joint link), and the moving space of the kinematic chains are determined on the basis of types of joints and their orientations. The multi-joint links set up the connecting among loops. The rows of the matrix are designed based on the independent loops, and the columns on the numbers of links n, the links elements in the matrix are ordered according to the direction of independent loops, the joints are expressed by prescribing letter or number, the orientation of joint is defined as the axes between two pairs of same link. The topological characteristic matrix is (2l+2)×n, and it is 3×n matrix for single loop kinematic chains. Examples show that all kinds of kinematic chains can be presented by the matrix. The matrix provides more topological information of kinematic chains with fewer elements. The matrix makes it easier to construct the corresponding structural sketch from the matrix elements, and it also provides an easy way for computer-aided kinematic and dynamic modeling.