In this paper, we give a full classification of all pentapods with mobility 2, where neither all platform anchor points nor all base anchor points are located on a line. Therefore, this paper solves the famous Borel–Bricard problem for two-dimensional motions beside the excluded case of five collinear points with spherical trajectories. But even for this special case, we present three new types as a side-result. Based on our study of pentapods, we also give a complete list of all nonarchitecturally singular hexapods with two-dimensional self-motions.

Issue Section:
Research Papers
Keywords:
Computational kinematics, Dual-quaternions, Kinematic geometry, Overconstrained mechanisms, Stewart-Gough platform
Topics:
Theorems (Mathematics), Mechanical admittance

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