The variants of general three-legged planar robot platforms are enumerated and classified. Constraint surfaces corresponding to individual platform legs in the kinematic mapping image space are classified and parametrized. The parametric equations are free from representational singularities. The entire set consists of hyperboloids of one sheet and hyperbolic paraboloids. This result corrects an oversight in the body of literature. These surfaces have important applications to the kinematic analysis of planar three-legged robot platforms, hence appropriate attention should be given to their classification.

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Keywords Constraint surface, Hyperbolic paraboloid, Hyperboloid of one sheet, Kinematic mapping, Planar parallel robot platform
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Journal Mechanism and Machine Theory
Hayes, M.J.D, & Husty, M.L. (M. L.). (2003). On the kinematic constraint surfaces of general three-legged planar robot platforms. Mechanism and Machine Theory, 38(5), 379–394. doi:10.1016/S0094-114X(02)00128-3