Position analyses of normal quadrilateral Assur groups

This paper presents position analyses of closed, quadrilateral normal Assur groups with different input joints. A closed quadrilateral normal Assur group is an Assur group of class c = 4 (as the greatest closed polygon is a quadrangle) and of order o = 4 (as there are four input joints). For an Assur group with r rotary input joints and p prismatic input joints, we write for short A(c, o)rp. For each of the four normal Assur groups A(4.4)40, A(4.4)31, A(4.4)22, A(4.4)13 and A(4.4)04 a position analysis is presented in analytical form. It is found that for a given set of system parameters the Assur groups A(4.4)40 and A(4.4)31 might theoretically adopt a maximum of 56 different (real or complex) positions while A(4.4)22 might adopt 40 different positions, A(4.4)13 24 positions, and A(4.4)40 12 positions. In all cases unlimited relative joint mobility is assumed.