Synthesis of the RSCR mechanism for four precision points with relaxed specifications

The maximum number of precision points that can be achieved by the RSCR mechanism is known to be three. However, in many practical applications, for example in pick-and-place tasks on an assembly line, four precision points are usually preferred. That is, the second and third precision points are used to control the departure and arrival motion of the first and the fourth precision points through their first derivatives. This paper presents an efficient technique for synthesizing the RSCR spatial mechanism to satisfy a set of two exact precision points plus two relaxed precision points, thereby allowing one degree-of-freedom of variability on the motion specifications.