Abstract
In this paper, we control the joints of a planar nR chain mechanically using RR dyads and obtain a one degree-of-freedom system that guides the end-effector smoothly through five specified task positions. To solve this problem, we specify the nR chain and determine it configurations when its end-effector is positioned in each of the five task positions. This yields a set of RR chain synthesis problems that constrain alternating links in a way that ensures that the relative joint angles required by the task positions are attained. In general, we cannot guaranteed that the resulting assembly will move smoothly between the task positions without jamming, however we present a strategy based on enforcing symmetry of the nR chain that yields useful solutions. Examples of constrained 311, 411, 511 and 611 are discussed. The procedure is general and can be applied to arbitrarily long serial chains.