A Novel Approach in the Direct Kinematics of Stewart Platform Mechanisms with Planar Platforms

Abstract

In handling the kinematic analysis of two rigid bodies connected to each other by six legs through the use of six double spherical joints, methods have been implemented both in the formulation and solution phases of the problem. A three-dimensional problem has been viewed, in fact, as a multitude of two-dimensional works on several planes, the intersections of which yield relationships allowing transition between adjacent planes. Thus formulation is purely based on the geometric structure consisting of eight planes of interest, ending in the three fundamental equations involving three angles between the base and side triangular planes. In solving the resulting three equations, an efficient strategy has been established to come up with 16 solution sets effectively. Extensions of the theory have been shown to include the analyses of other Stewart platform models. Efficiency and effectiveness of the approach has been verified on numerical examples.

Partially Flagged Parallel Manipulators: Singularity Charting and Avoidance

“…One of them corresponds to the well-known octahedral manipulator [see Fig. 1(a)] whose forward kinematics is quite involved as it amounts to solving an eighth-degree polynomial, leading to 16 solutions or assembly modes [8], [20], [21]. On the contrary, the forward kinematics of the other two can be solved by a sequence of three consecutive trilaterations, leading to eight solutions [10]- [12].…”

Forward Displacement Analysis of a General 6‐3 Stewart Platform Using Conformal Geometric Algebra

“…In fact, the principle of Liang's method is the same as that in [4]. Both Nanua et al [6] in 1990 and Akçali and Mutlu [7] closed-form direct kinematic solution of the 6-3SPS using the tetrahedron approach in 2011. The closed-form solution in [8], however, is not polynomial form.…”

The octahedral manipulator revisited

“…In all cases the polynomial variable is the tangent of onehalf the angle defined by the plane supporting P 1 P 2 P 4 (alternatively P 2 P 3 P 5 , or P 3 P 1 P 6 ) and the base plane. More recently, Akçali and Mutlu revisited the problem -also using resultant elimination and tangent-half-angle substitution techniques-with the aim of reducing the computational cost of evaluating the resulting univariate polynomial [14]. Finally, it is worth to mention that the forward kinematics of the octahedral manipulator has also been solved locally using Newton-Raphson iterative schemes.…”