On the Derivation of Grashof-Type Movability Conditions With Transmission Angle Limitations for Spatial Mechanisms

Derivation of Grashof-type movability conditions for spatial mechanisms that may include transmission angle limitations is discussed. It is shown that in general, different conditions must be derived for each configuration (branch) of a mechanism. In the absence of transmission angle limitations, the conditions become identical for pairs of configurations. As an example, Grashof-type conditions that ensure crank rotatability, existence of drag link type of mechanisms, the presence of single or multiple changeover points, and the possibility of full rotation at intermediate revolute joints are derived for a spatial RRRSR mechanism. The problems involved in such derivations, the use of approximation techniques, and a number of related subjects are discussed.