Trajectory Planning for Robotic Belt Grinding Based on Curvature Optimization

Aiming at the problems of low programming efficiency and machining precision of belt grinding for complex surface parts, a method is proposed to generate a grinding path for industrial robots according to the curvature values of key contact points, based on the reconstructions of B-spline curves and surfaces and the robot off-line programming technique. Firstly, the B-spline basis functions of the grinding trajectory are calculated by the knot vectors constructed with the key contact points on the surfaces of parts for belt grinding and the accumulation chord length parameter method. Secondly, all unknown control points and cubic B-spline machining curves are obtained according to the inverse matrix of the control points. Thirdly, the key points are refined to produce the target points conforming to grinding process requirements by analyzing the curvature variation rate and arc length between key contact points. Finally, the processing postures of the target points are obtained according to the solution of bi-cubic B-spline interpolation surface equations. Test results of faucet grinding show that the curvature optimization algorithm is obviously better than the section method in term of the contour shape of the workpiece surface, and its roughness value can be stabilized at about 0.082 μm, which effectively improve the surface processing quality of workpieces.