ASSEMBLABILITY, CIRCUITS, BRANCHES, LOCKING POSITIONS, AND ROTATABILITY OF INPUT LINKS OF MECHANISMS WITH 4 CLOSURES

A general analytical treatment is provided for determining conditions for assemblability, rotatability of input links, locking positions, an d number of circuits of mechanisms with four closures and quartic inpu t-output displacement polynomial. It is shown that assemblability, rot atability of input cranks, and lock positions are branch dependent pro perties for mechanisms with four closures and in general such mechanis ms can have many branch dependent circuits. Such mechanisms may be ass emblable for only two branches (instead of all four) and the input lin k rotatability is not only branch dependent but also starting position and direction of motion dependent. The input link may be continuously rotatable for one branch while for other branch it may go through one cycle of rotation (>2pi but less than 4pi) and then experience a lock ing position. A detailed analysis of assemblability, branching, lockin g positions, circuits, and rotatability is presented for spatial five- link RRRSR, RPRSR, RRPSR, and PRRSR mechanisms.