The position analysis of Assur kinematic chain with five links

The position analysis for all six types of 5-link chain, classified based on the different combination of revolute and prismatic joints, is presented. Any 5-link is first dismantled at a chosen revolute or prismatic joint and separated into a four-bar and a binary link. The breaking point/line then must lie on the intersection points of two curves generated by the coupler point/line on the four-bar and by the binary link. By analyzing the intersection of both curves with the aid of Bezout number and circularity as well as multiple points of curves, the maximum number of the possible solutions of the breaking point/line is evaluated. The possible configurations of a 5-link can then be obtained after solving the algebraic equations of both curves. Numerical examples are given and some special cases are also discussed.