Double configurations of five-link Assur kinematic chain and stationary configurations of Stephenson six-bar

A five-link Assur kinematic chain (AKC) has six configurations at most. If two of them are identical, they are defined as double configurations. The five-link AKC is dismantled into a four-bar and a binary link for analyzing the double configurations. The feature for the occurrence of double configurations is the gradient vector of coupler curve being parallel to the binary link. An equation is thus derived and combined with the coupler curve equation of four-bar to solve the coordinates of dismantling point. The tasks such as finding the specific length of a binary link and coordinate of a fixed pivot are discussed. The maximum number of solutions is figured out on the basis of Bezout number, circular points, and double points. These results are then applied to find the stationary configurations or limiting positions for Stephenson six-bar. The maximum number of limiting positions for each concerned link is found as 24. The five-link AKC and six-bar with prismatic joints included are also considered. (c) 2006 Elsevier Ltd. All rights reserved.