2026-10-14T05:12:44Z https://api.figshare.com/v2/oai

oai:figshare.com:article/33974473 2026-09-23T17:53:13Z portal_1056 item_type_3 month_year_09_2026

Higher-order Singularities of Two-Loop 3(RR) Planar Mechanisms including 3(RPR) and 3(RRR) Planar Robots Charles Wampler (25111128) Manfred Husty (25098786) Jonathan Hauenstein (17332201) Martin Pfurner (25098790) 3RPR robot Singularity planar pentad multiplicity direct kinematics numerical algebraic geometry <p dir="ltr">The direct kinematics problem of an n-degree-of-freedom mechanism requires solving for all assembly configurations of the mechanism when n joint inputs are given, which is equivalent to solving the direct kinematics of a rigid structure. We consider the case where that structure is a planar pentad, also known as a 3(RR) mechanism, which is the only two-loop planar structure that does not decompose into two triangles. In particular, we study the cases where the direct kinematics of the pentad is singular, so that the structure has an isolated solution with multiplicity greater than one, often referred to as a mechanism with infinitesimal motion or as a "shaky'" mechanism. We give a complete analysis of singularities having multiplicities 3 and 4 arising in the direct kinematics of (3RPR) and (3RRR) planar robots, and also give complete solutions for problems of constructing pentads having multiplicities 4, 5, or 6 by adding a third center-point/circle-point pair to a given four-bar linkage. This builds on the work on the multiplicity 6. When elastic deformation of links and clearance in joints are present, as is always the case in actual mechanisms, pentads with higher-order singularities move through a finite range of motion, which makes them candidates for practical designs, including for compliant mechanisms.</p> 2026-09-23T17:53:13Z Dataset Dataset 10.7274/33974473.v1 https://figshare.com/articles/dataset/Higher-order_Singularities_of_Two-Loop_3_RR_Planar_Mechanisms_including_3_RPR_and_3_RRR_Planar_Robots/33974473 CC BY 4.0