Comparing theoretically modeled stiffness with experimentally measured stiffness using geometric invariants

The study investigates primarily the validity of a proposed stiffness model of a 6-DOF in-parallel compliant mechanism (hexapod machine or Stewart Platform). The mechanism is a good example for demonstrating the theory of stiffness mapping to control the force and position for a robot manipulator. An analysis of stiffness mappings may be essential to assess the quality of force and position control for robot manipulators.;A 6-DOF in-parallel compliant mechanism is integrated with a GE-P60 robot to perform an experiment for the measurement of twist and wrench matrices. The experimental results are used to check the validity of the proposed theoretical stiffness model. A geometrically meaningful methodology is developed for this comparison. The method implements geometric invariants for comparing a pair of like geometric entities and is applied to active plane transformations and stiffness mappings. This study demonstrates that there are no more than twenty-four parameters available for comparing one stiffness mapping with another. When utilizing stiffness matrices using geometric invariants, the comparison involves four independent quantities: eigenvalues, screws' pitches, angles between screws, and perpendicular distances between screws. All of these quantities have distinct dimensions and are, therefore, incompatible. No factor can be assigned to scale all of them to yield a unique quantity with geometric meaning.;The equivalent stiffness matrices could be defined by means of equivalent wrench matrices according to the wrench effects when a twist matrix is applied to the compliant system. This definition characterizes the physical effect occurring in the given systems.;Geometric invariants, equivalent wrench effects, and the reciprocal product of a twist screw and a wrench screw are used to investigate the relationship between the theoretical and experimental stiffness mappings. The results show good correlation. A 6-DOC wrench control using the proposed theoretical stiffness model is performed to examine the capability of a 6-DOF in-parallel compliant mechanism in compliant motions. The proposed theoretical model was found to be reliable in predicting the performance characteristic (wrench and twist) of a 6-DOF in-parallel compliant mechanism.