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General methods based on inverse kinematics are presented to develop singularity-free compatible workspaces for three degrees-of-freedom parallel manipulators. The characteristics of boundary surfaces are investigated. A workspace boundary surface consists of six or more patches generated by different sets of constraint equations. Each set includes one equation from boundary constraints and several equations from inverse kinematic constraints. The equations for all the patches can be determined by solving direct kinematics once and three times, respectively, for symmetrical and non-symmetrical manipulators. The methods are applicable to existing 3-limb special manipulators with simple inverse kinematics and general 3-limb manipulators without any spherical joints. The effect of passive joint limits, link interactions and singularity are considered in the proposed methods.

Determination of the Singularity-Free Compatible Reachable Workspace for Different Types of Three Degrees-of-Freedom Parallel Manipulators