Kinemato-geometrical methodology for analyzing curvature and torsion of trajectory curve and its applications

A kinemato-geometrical methodology for analyzing the curvature and torsion of the trajectory curve is developed, and the formulas for computing them and their arc-rates of change are derived. The applications of the derived formulas in spatial kinematics are narrated. The equations of axodes are developed, and the formulas for computing their common unit normal and GAVs are enumerated. An exemplary application of the IHP curve in the synthesis of a 2-loop 2H-C-3S type spatial mechanism for body guidance is illustrated.