Design of hip joint assistant asymmetric parallel mechanism and optimization of singularity-free workspace

This paper presents an asymmetric fully constrained parallel mechanism prototype that has three rotation degrees of freedom and three actuations. The mechanism employs pantographs as three-rotation constrained leg instead of normal RRR-leg to avoid disadvantages like singularity, uncertainty or interference with other legs. Reciprocal results based on Grassmann geometry are categorized, and used for analyzing surfaces whose Jacobian matrix determinant is zero. Angle derived from reciprocity is used for its straight geometry meanings. Larger angle would push singularity away from workspace and has maximum value of 90°. The results showed that the design has desired freedoms, and angle has monotone increasing relation with the determinant of Jacobian that could avoid singularity and afford a rapid way for future optimization.