Force-reflected teleoperation with in-parallel devices are gaining prominence in robotics applications. Although their development has been limited primarily to Stewart-platform type devices, many other in-parallel hand controllers hold promise for force-reflected manipulation. One factor prohibiting a full exploration involves their singularity analyses-use of conventional rank determining methods are overly complicated. Singularity analysis complications arise because the Jacobian matrix has several functionally dependent variables. In this analysis, we first derive the Jacobian matrix and then show its six columns can be viewed as zero-pitch wrenches (lines) acting on the top platform. We then show how line geometry and rank determining geometric constructions can be used to obtain all configuration singularities.
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