Sandipan Bandyopadhyay

Trajectory-tracking control of parallel manipulators is more difficult than in the case of serial ones due to the presence of the loop-closure constraints and constraint forces resulting from them. One needs to eliminate these forces to get to the equation of motion, and then apply a control scheme. In this paper, such a control scheme is presented through application on a semi-regular Stewart platform manipulator (SRSPM). The manipulator has six degrees-of-freedom; however, it is modelled by a system of 18 coupled nonlinear ordinary differential equations (ODE) using the constrained Lagrangian formulation. The model is then linearised through feedback, and controlled by a linear PD servo scheme. Numerical simulations over a non-singular path show that the scheme is fairly accurate, at the cost of being computationally expensive. The scheme is general in nature, and as such, it is expected to work in the case of other parallel manipulators as well.

This paper presents the computation of the safe working zone (SWZ) of a parallel manipulator having three degrees of freedom. The SWZ is defined as a continuous subset of the workspace, wherein the manipulator does not suffer any singularity, and is also free from the issues of link interference and physical limits on its joints. The proposed theory is illustrated via application to two parallel manipulators: a planar 3-RRR manipulator and a spatial manipulator, namely, MaPaMan-I. It is also shown how the analyses can be applied to any parallel manipulator having three degrees of freedom, planar or spatial.

This paper presents a formulation to identify a sphere in the fixed-orientation workspace of a Stewart platform manipulator, such that no pair of legs of the platform would suffer an interference between them, if the geometric centre of the moving platform remained inside this sphere. Identification of such a sphere is an important step in the design and analysis of such manipulators. The geometric formulation leads to certain algebraic equations, and finally to the solution of a degree 8 univariate equation. The mathematical formulation is applied to two different situations, and the results obtained are verified by comparison with those obtained from an established open-source library designed to detect interference between solids.

This paper presents a formulation to identify a sphere in the fixed-orientation workspace of a Stewart platform manipulator, such that no pair of legs of the platform would suffer an interference between them, if the geometric centre of the moving platform remained inside this sphere. Identification of such a sphere is an important step in the design and analysis of such manipulators. The geometric formulation leads to certain algebraic equations, and finally to the solution of a degree 8 univariate equation. The mathematical formulation is applied to two different situations, and the results obtained are verified by comparison with those obtained from an established open-source library designed to detect interference between solids.

A two-degree-of-freedom RSSR-SSR manipulator is proposed for the sun-tracking application. A detailed study of its forward and inverse kinematic problems is presented. It is illustrated through an example that the requisite range of motion can be achieved for exact tracking at the chosen location without encountering singularities or violating the limits of commercially available spherical joints. Static analysis is also performed to show that the load is significantly distributed among the two limbs, thereby reducing the strength requirement on the foundations at base pivots.

Determination of the safe working zone (SWZ) of a parallel manipulator is a one-time computational task with several permanent benefits. As this subspace of the workspace of the manipulator is free of both the loss- and gain-type singularities, link interference, as well as physical joint limits, the manipulator can move freely in this space. Moreover, if the natural choice of a convex-shaped SWZ is adhered to, then point-to-point path planning inside the SWZ always has a trivial solution, namely, a segment joining the two points, which is guaranteed to be inside the workspace. In this paper, the SWZ of the 3-RRS existing in the İzmir Institute of Technology has been computed. Starting with the geometry of the manipulator, the loop-closure constraint equations have been derived. The singularity conditions are obtained based on the singularity of certain Jacobian matrices associated with the constraint functions. The interference between the links are detected by first encapsulating the links in rectangular parallelepipeds, which are then discretized into triangles, and subjected to collision tests between the relevant pairs of triangles. Using these theoretical developments, the SWZ is computed. The numerical results are depicted graphically.

Identification of the safe working zone (SWZ) of a parallel manipulator can be an important part of its path-planning process or design. Computationally efficient and accurate methods are required to make these demanding calculations practically feasible. This paper looks at the Cartesian and polar variants of a 2-D numerical scanner which are applicable for 3-degrees-of-freedom (DoF) planar or spatial parallel manipulators and presents a detailed analysis of their relative speeds, advantages and disadvantages, based on a case study involving the spatial 3 -RRS manipulator. Results of such a study provide the analysts with a deeper understanding of the functioning of the scanner, which in turn, helps the computation of the SWZ of other manipulators in a fast and reliable manner.