Position analyses of open normal assur groups A (3.6)

This paper presents position analyses of open normal Assur groups A (3.6). Planar mechanisms can be seen as composed of link groups (Assur groups) with zero mobility relative to the links to which they are successively added. These Assur groups, serving as modules in the synthesis and analysis of complex planar mechanisms, might adopt a certain number of positions which allow choosing different solutions to the engineering task. An open normal Assur group, for which we write A (3,6) in short, is an open (non-closed) linear kinematic chain of ternary (3) links to which 6 binary links are attached. It is found that for a given set of system parameters an open normal Assur group A (3.6) held together exclusively by rotor joints might theoretically adopt 162 different positions (real and complex). If the outer joints at the binary links are prismatic joints, the number of possible positions is reduced to 16.