The closed-loop real-time feedback control requires the forward kinematics analysis, which has not been solved completely in the field of parallel robots. A system of high degree univariate polynomial equations of the analytical forward kinematics analysis of 6-UPS parallel manipulators (6-UPS) can be obtained by eliminating variables. Also they can be analyzed by adding at least 2 extra displacement sensors. Although with this progress, it is still not capable to be applied to the real-time closed-loop feedback control. In order to achieve the closed-loop feedback control with high performance, a new analytical algorithm is proposed. In the new algorithm, only one displacement sensor is installed in the center of 6-UPS to obtain the seventh rod length, the elements of rotation matrix based on quaternions are replaced by new symbols, and the 11 compatible equations can be solved by reducing the degree twice and then raising the degree of the equations' variables combining with algebraic elimination methods. The analytical forward kinematics solutions of 6-UPS, which is needed by the closed-loop real-time feedback control system, are obtained in the end. Taking advantages of the proposed method, the singularity problem is solved and the multi-solution problem is also solved because unique position and orientation can be obtained. Finally, one numerical example is presented and the result is verified. Results indicate that the proposed forward kinematics algorithm is both correct and effective.
LIU Yanli
,
CHENG Shili
,
JIANG Surong
,
YANG Xiaolong
,
LI Yao
,
WU Hongtao
. Forward Kinematics of 6-UPS Parallel Manipulators with One Displacement Sensor[J]. Journal of Mechanical Engineering, 2018
, 54(5)
: 1
-7
.
DOI: 10.3901/JME.2018.05.001
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