An algebraic formulation of static isotropy and design of statically isotropic 6–6 Stewart platform manipulators

Abstract

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulator is identified analytically.We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration.

Semi-isotropic design of a Stewart platform through constrained optimization

“…An SRSPM shown in Figure 1 has a stationary semi-regular hexagonal bottom platform and another semi-regular hexagonal movable top platform. 15–17 Six linear actuators are shown in the figure as b i t i with i = 1 to 6, where b i are the bottom joints located at a radius r b and t i are the top joints located at a radius r t . While the bottom joints are meant for connecting each limb with the stationary base platform BP about the semi-regular hexagon b 1 b 2 b 3 b 4 b 5 b 6 , the top joints connect the other ends of the respective limbs with the semi-regular hexagonal moving platform MP with the vertices t 1 , t 2 , t 3 , t 4 , t 5 , and t 6 .…”

“…In view of the fact that the minimum singular value achievable under heaving and yawing corresponding to the generalized translational motion is 2 times the other modes, a diagonal matrix 17 is introduced so as to make each matrix on the right-hand side of equation (10a) proportional to the matrix D involving proportionality σ1 2, σ2 2, σ3 2 and σ4 2 respectively leading to and …”

“…However, the impossibility of achieving perfect isotropy by a mechanically feasible design of a Stewart platform was discussed by several investigators. 15–18 By a nonlinear least-square minimization, it was found 15 that the minimum attainable condition number for a Stewart platform in generalized translational motions could be 2. In later studies, 14,19 a normalized Jacobian with dimensionally homogeneous elements were arrived by dividing the elements with suitable scale factors contained in a matrix.…”

Track-position and vibration control simulation for strut of the Stewart platform

“…Each of the six struts is designed to be identical to the others, both mechanically and electromechanically. It has been illustrated that each strut can be decoupled if the Stewart platform deliberately employs a special geometry or is particularly located, for example, in an orthogonal configuration, or if the instrument is located in the central axis (Bandyopadhyay and Ghosal, 2009). Considering the use of PZT and VCM and viscoelastic material in the architecture of a single strut, a vibration control measure of the active-passive series isolation system is designed.…”

A Dimensional Design Problem of a Parallel Manipulator for the Space Docking Test System According to a Prescribed Workspace and Performance Indices

“…The ground-based docking/capture test system has been investigated by many researchers [1][2][3]. And most of them use the Stewart platform for spacecraft docking simulation due to the fact that parallel manipulators have better load-carrying capacity, better stiffness, and better precision than serial manipulators [4][5][6]. To design a parallel manipulator, the first step is to design the structure for the manipulator, this is called the type synthesis [7][8][9].…”