A general analytical treatment is provided for determining conditions for assemblability, rotatability of input links, locking positions, and number of circuits of mechanisms with four closures and quartic input-output displacement polynomial. It is shown that assemblability, rotatability of input cranks, and lock positions are branch dependent properties for mechanisms with four closures and in general such mechanisms can have many branch dependent circuits. Such mechanisms may be assemblable for only two branches (instead of all four) and the input link 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 (>2π but less than 4π) and then experience a locking position. A detailed analysis of assemblability, branching, locking positions, circuits, and rotatability is presented for spatial five-link RRRSR, RPRSR, RRPSR, and PRRSR mechanisms.

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