Measuring curvature of trajectory traced by coupler of an optimal four-link spherical mechanism

This research paper presents design of a gripper finger mechanism and a new curvature measurement method of fingertip trajectory. Firstly, the conditions of a grasp provided by gripper, which was designed from a spherical mechanism, was explained. Therefore, trajectory length of coupler point was modeled as objective function which is maximized. Ball-Burmester theory was used to form constraints which can provide a spherical curve with curvature close to zero. A plausible dimension range of mechanism, transmission angle, instantaneous invariants were arranged as constraint function. A meta-heuristic algorithm previously developed by one of authors was used to search the best instantaneous invariants based on the type of mechanism. The optimal solution was prototyped, and three-fingered gripper assembled. Secondly, an endoscopic camera peculiarly was used to measure curvature of the trajectory traced by coupler point of an optimal four-link spherical mechanism which was supposed to compose a finger of a robotic gripper. The coupler of the mechanism was expected to trace approximately a great circle arc to provide a grasp. Therefore, the technique to measure curvature was based on image processing and geodetic curvature theory. A calibrated endoscopic camera was used for acquisition of video record above the prototype which was centered in the center of the camera screen. The curvature of coupler point of optimal spherical mechanism design and prototype were compared. According to performed regression analysis, results of the measurement were %97 reliable for the useful part of the trajectory.