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Title: Minimum-jerk trajectory planning pertaining to a translational 3-degree-of-freedom parallel manipulator through piecewise quintic polynomials interpolation
Authors: Lu, S
Ding, BX
Li, Y 
Issue Date: 2020
Source: Advances in mechanical engineering, 1 Mar. 2020, v. 12, no. 3, p. 1-18
Abstract: This article aims to present a minimum-jerk trajectory planning approach to address the smooth trajectory generation problem of 3-prismatic-universal-universal translational parallel kinematic manipulator. First, comprehensive kinematics and dynamics characteristics of this 3-prismatic-universal-universal parallel kinematic manipulator are analyzed by virtue of the accepted link Jacobian matrices and proverbial virtual work principle. To satisfy indispensable continuity and smoothness requirements, the discretized piecewise quintic polynomials are employed to interpolate the sequence of joints' angular position knots which are transformed from these predefined via-points in Cartesian space. Furthermore, the trajectory planning problem is directly converted into a constrained nonlinear multi-variables optimization problem of which objective function is to minimize the maximum of the joints' angular jerk throughout the whole trajectory. Finally, two typical application simulations using the reliable sequential quadratic programming algorithm demonstrate that this proposed minimum-jerk trajectory planning approach is of explicit feasibility and appreciable effectiveness.
Keywords: Trajectory planning
Parallel kinematic manipulator
The principle of virtual work
Piecewise quintic polynomials
Publisher: SAGE Publications
Journal: Advances in mechanical engineering 
ISSN: 1687-8132
EISSN: 1687-8140
DOI: 10.1177/1687814020913667
Rights: The Author(s) 2020
Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License ( which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (
The following publication Lu, S., Ding, B., & Li, Y. (2020). Minimum-jerk trajectory planning pertaining to a translational 3-degree-of-freedom parallel manipulator through piecewise quintic polynomials interpolation. Advances in Mechanical Engineering. is available at
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