Improved trajectory planning of an industrial parallel mechanism by a composite polynomial consisting of Bézier curves and cubic polynomials

Abstract A new composite polynomial is generated, to be used in the trajectory planning of a 2-dof parallel mechanism; by combining cubic polynomials with Bezier curves based on quadratic Bernstein polynomials. By the cubic polynomials, a smooth trajectory is obtained in the vicinity of the starting and ending points, while a better convergence is obtained to the via points by the Bezier curves. The position, velocity, and acceleration profiles obtained using this new polynomial are compared with those obtained using the cubic polynomial spline method. The position, velocity, and acceleration profiles achieved by the new polynomial are smoother; and more, maximum speed and acceleration values are lower than those obtained by the cubic spline method. Due to these lower values, lower capacity actuators may be utilized and the life of the actuators may be extended. On the other hand, the continuous acceleration curve of the composite polynomial will prove less jerky motion, which means less vibration. It is also possible to indicate energy saving potential when considering the speed-torque characteristic curves of servomotors. Finally, a working prototype is manufactured and real-time experiments are carried out to demonstrate the validity and competency of the proposed composite polynomial approach.