The ball joint, often referred to as a spherical or `S' joint is modeled using dual-number coordinate-transformation matrices. The joint consists of concave and convex spherical surfaces engaged to prevent translations but allowing three degrees of freedom, all of which are rotations. Derivative-operator matrices to be used in the Fischer-Paul adaptation of the Uicker-Denavit-Hartenberg numerical scheme for displacement analysis of spatial mechanisms are developed. The generalized slider-crank (CSSP) mechanism is presented as an example featuring ball joints where coordinate-transformation matrices modeling links with ball joints are used in a concatenation with analogous matrices modeling links with revolute, prismatic or cylindrical joints to analyze the displacements.
All Science Journal Classification (ASJC) codes
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications