Numerical direct kinematic analysis of fully parallel linearly actuated platform type manipulators. (English) Zbl 1049.70003

Without referring to the main references in the area [e.g. J.-P. Merlet, Parallel robots. Solid mechanics and its applications. 74. Dordrecht: Kluwer (2000; Zbl 0983.70002); M. Husty, Mech. Mach. Theory 31, 365–380 (1996)], the paper discusses a numerical approach to the direct kinematics of two types of linearly actuated fully parallel platform manipulators. A two-step approach is suggested. In a first step an approximate solution to the direct problem is found via nonlinear programming using a linear spring model for the lengths of the legs and optimizing an objective function that essentially sums the squares of the differences of actual lengths of the legs and the lengths of the springs. In a second step, a Newton-Raphson approach is chosen to refine the search. In two examples the performance of the proposed algorithm is demonstrated. Nothing is said about the performance close to singularities.


70B15 Kinematics of mechanisms and robots
70-08 Computational methods for problems pertaining to mechanics of particles and systems
53A17 Differential geometric aspects in kinematics


Zbl 0983.70002
Full Text: DOI


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