A novel five-axis real-time interpolation algorithm for 3[PP]S-XY hybrid mechanism is proposed in
this paper. In the algorithm, the five-axis tool path for controlling this hybrid mechanism is separated into two
sub-paths. One sub-path describes the movement of 3[PP]S parallel kinematic mechanism module, and the other
one describes the movement of XY platform. A pair of cubic Bezier curves is employed to smooth the corners in
those two sub-paths. Based on the homogenous Jacobian matrix of 3[PP]S mechanism, a relationship between
the position errors of every driving joint in hybrid mechanism and the position deviation of the tool tip center
point at the moving platform is established. This relationship is used to estimate the approximation error for
the corners smoothing according to the accuracy requirement of tool tip center in interpolation. Due to the high
computational efficiency of this corner smoothing method, it is integrated into the look-ahead module of computer
numerical control (CNC) system to perform online tool path smoothing. By performing the speed planning based
on a floating window scheme, a jerk limited S-shape speed profile can be generated efficiently. On this basis, a realtime
look-ahead scheme, which is comprised of path-smoothing and feedrate scheduling, is developed to acquire a
speed profile with smooth acceleration. A monotonic cubic spline is employed for synchronization between those
two smoothed sub-paths in tool path interpolation. This interpolation algorithm has been integrated into our
own developed CNC system to control a 3PRS-XY experimental instrument (P, R and S standing for prismatic,
revolute and spherical, respectively). A club shaped trajectory is adopted to verify the smoothness and efficiency
of the five-axis interpolator for hybrid mechanism control.
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