Robots Based on Assur Group A (3.5)

Abstract

The paper presents position analyses of open normal Assur groups A (3.5). Planar mechanisms can be considered to be composed of link groups (Assur groups) with zero mobility relative to the links to which they are successively added. These Assur groups, which serve as modules in the synthesis and analysis of complex planar mechanisms, might adopt a certain number of positions which allow choosing different solutions for the engineering task. An open normal Assur group, for which we write A (3.5) in short, is an open kinematic chain of ternary links to which 5 binary links (legs) are attached. It is found that for a given set of system parameters an open normal Assur group A (3.5) held together exclusively by rotor joints might theoretically adopt a maximum of 54 different positions (real and complex). If the input rotor joints at the 5 legs of this Assur group are successively exchanged by 1, 2, 3, 4, or 5 prismatic input joints, then the number of its possible positions becomes 54, 46, 28, 16 or 8. An open Assur group A (3.5) might serve as a basic mechanism for a parallel redundant planar robot.