Linear Pentapods with a Simple Singularity Variety
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There exists a bijection between the configuration space of a linear pentapod and all points (u,v,w,p_x,p_y,p_z)∈R^6 located on the singular quadric Γ: u^2+v^2+w^2=1, where (u,v,w) determines the orientation of the linear platform and (p_x,p_y,p_z) its position. Then the set of all singular robot configurations is obtained by intersecting Γ with a cubic hypersurface Σ in R^6, which is only quadratic in the orientation variables and position variables, respectively. This article investigates the restrictions to be imposed on the design of this mechanism in order to obtain a reduction in degree. In detail we study the cases where Σ is (1) linear in position variables, (2) linear in orientation variables and (3) quadratic in total. The resulting designs of linear pentapods have the advantage of considerably simplified computation of singularity-free spheres in the configuration space. Finally we propose three kinematically redundant designs of linear pentapods with a simple singularity surface.
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