TY - JOUR
T1 - A simple approach to solving the kinematics of the 4-UPS/PS (3R1T) parallel manipulator
AU - Gallardo-Alvarado, Jaime
AU - García-Murillo, Mario A.
AU - Islam, Md Nazrul
AU - Abedinnasab, Mohammad H.
N1 - Publisher Copyright:
© 2016, The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg.
PY - 2016/5/1
Y1 - 2016/5/1
N2 - This work reports on the position, velocity and acceleration analyses of a four-degrees-of-freedom parallel manipulator, 4-DoF-PM for brevity, which generates Three-rotation-one-translation (3R1T) motion. Nearly closed-form solutions to solve the forward displacement analysis are easily obtained based on closure equations formulated upon linear combinations of the coordinates of three non-collinear points embedded in the moving platform. Then, the input-output equations of velocity and acceleration of the robot manipulator are systematically established by resorting to the theory of screws. To this end, the Klein form of the Lie algebra se(3) of the Euclidean group SE(3) is systematically applied to the velocity and reduced acceleration state in screw form of the moving platform cancelling the passive joint rates of the parallel manipulator. Numerical examples, which are confirmed by means of commercially available software, are provided to show the application of the method.
AB - This work reports on the position, velocity and acceleration analyses of a four-degrees-of-freedom parallel manipulator, 4-DoF-PM for brevity, which generates Three-rotation-one-translation (3R1T) motion. Nearly closed-form solutions to solve the forward displacement analysis are easily obtained based on closure equations formulated upon linear combinations of the coordinates of three non-collinear points embedded in the moving platform. Then, the input-output equations of velocity and acceleration of the robot manipulator are systematically established by resorting to the theory of screws. To this end, the Klein form of the Lie algebra se(3) of the Euclidean group SE(3) is systematically applied to the velocity and reduced acceleration state in screw form of the moving platform cancelling the passive joint rates of the parallel manipulator. Numerical examples, which are confirmed by means of commercially available software, are provided to show the application of the method.
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U2 - 10.1007/s12206-016-0439-4
DO - 10.1007/s12206-016-0439-4
M3 - Article
AN - SCOPUS:84971653755
SN - 1738-494X
VL - 30
SP - 2303
EP - 2309
JO - Journal of Mechanical Science and Technology
JF - Journal of Mechanical Science and Technology
IS - 5
ER -