Sandipan Bandyopadhyay

The 3-RRS parallel manipulator presented in this study comprises of parallel revolute joint axes in each leg. The manipulator is composed of a base and a moving platform which are in the shape of equilateral triangles. Moving platform has two rotational and one translational degrees-of-freedom. This study formulates the forward and inverse kinematics of the parallel manipulator. A 16th order polynomial in terms of one of the passive joint variables is obtained for the forward kinematic analysis. Numerical results and the corresponding pose of the manipulator for inverse and forward kinematics are presented.

This paper presents a comparative study between two related methods of formulating the equations of motion, within the Lagrangian framework, for closed-loop mechanisms. Such mechanisms encounter singularities not only at the boundaries of their workspaces, but also inside the workspaces. The latter kind of singularities are detrimental to the operation of the mechanisms and may lead to their mechanical failure. The primary objective of the paper is to investigate the ways in which these singularities impact the two formulations, and to establish a relation between them. A planar five-bar mechanism is used to illustrate that the singularities appearing in one formulation is a subset of those appearing in the other formulation. The second objective is to provide a qualitative analysis of the time-complexities of the respective formulations. A planar five-bar and the Stewart platform manipulator are used to study and compare the computational costs incurred in either of the formulations.

The planar 3-RRR parallel manipulator is known to have six assembly modes. However, analysing it in the framework of spatial kinematics reveals that it has a total of twelve assembly modes, six in each of the two possible operation modes. The modes are derived using a Study parameter formulation first, and later confirmed in another formulation in the joint-space, and finally visualised in terms of the planar constraint curves generated by the sub-chains of the manipulator. Numerical results show that all the twelve modes can be real for certain inputs.

This paper presents a method to compute the largest possible cylindrical volume within the translational workspace of the semi-regular Stewart platform manipulator (SRSPM), which would be free of gain-type singularities. An analytical approach is used in finding the singularity-free regions rather than discretising the workspace into small singularity-free volumes. Comparison with another convex shape, i.e., the sphere, is performed to demonstrate the relative importance and usefulness of using the cylindrical geometry for finding the singularity-free spaces.

For repetitive material-handling operations in various industries, fixed automation using single-degree-of-freedom mechanisms can often serve as a low-cost alternative to multi-degrees-of-freedom robots. Therefore, developing design procedures for inexpensive fixed automation solutions may be highly relevant in the context of developing as well as underdeveloped economies. A design methodology to analytically synthesise a planar pick-and-place system for displacement and velocity requirements using a planar four-bar mechanism is carried out in this work. A methodology to establish the availability of kinematic defect-free solutions in terms of two free design parameters is also proposed and illustrated with a numerical example.

This paper presents a comprehensive analytical solution to the forward kinematic problem of a newly introduced spatial parallel manipulator, namely, the 3-RPRS. The manipulator has three legs with two actuators in each, which connect a moving triangular platformto a fixed base. Loop-closure equations are formed to find the unknown passive rotary joint angle in each leg. These equations are subsequently reduced to a single univariate polynomial equation of degree 16. The coefficients of this equation are obtained as closed-form functions of the architecture parameters of the manipulator and the input joint angles, and therefore the analysis covers all possible architectures and configurations. Furthermore, it is found that the polynomial has only the even powers, therefore leading to 8 pairs of solutions, each pair being mirrored at the base platform. The theoretical developments are illustrated via a numerical example. The results obtained are validated by checking the residues of the original loop-closure equations, thereby establishing the correctness of the formulation as well as the results.

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.

The double-wishbone (DWB) is a popular suspension system, particularly in the high-end automobiles. Simulation of its kinematics and dynamics are vital elements in the process of analysis and design of these complex mechanical systems. However, the simulation of the DWB suspension can be computationally demanding, due to the large number of nonlinear, coupled ordinary differential equations (ODEs) that arise from the motion of the multiple links present in the system. In this paper, a less common approach to the Lagrangian formulation is adopted, which is known as the embedded formulation or the actuator space formulation. In this formulation, the number of ODEs to be solved come down to only two-a number that equals the degree-of-freedom of the system. The joint variables associated with the unactuated links are computed through the forward kinematics of the system. This method has the advantage of reducing the computational burden in the numerical solution of the ODEs significantly, as the number of ODEs comes down to two, as opposed to eleven in the more commonly used configuration space formulation. Furthermore, the unactuated variables are determined from the kinematic constraints, as opposed to being computed from the numerical solutions to ODEs, which make them more accurate. The formulation is illustrated via numerical examples implemented in the Computer Algebra System (CAS), Mathematica. It is believed that such a formulation would aid in the understanding of the dynamics of the suspension systems, and help in the process of their design.

This paper presents an application of multi-objective optimisation for the design of an important component of automobiles, namely the suspension system. In particular, we focus on the double wishbone suspension, which is one of the most popular suspensions in use today and is commonly found on mid-range to high-end cars. The design of such mechanical systems is fairly complicated due to the large number of design variables involved, complicated kinematic model, and most importantly, multiplicity of design objectives, which show conflict quite often. The above characteristic of the design problem make it ideally suited for a study in optimisation using non-classical techniques for multi-objective optimisation. In this paper, we use +NSGA-II+ [5] for searching an optimal solution to the design problem. We focus on two important performance parameters, namely camber and toe, and propose objective functions which try to minimise the variation of these as the wheel travels in jounce and rebound. The pareto-optimal front between these two objectives are obtained using multiple formulations and their results are compared. © 2010 Springer-Verlag.

This paper presents a novel geometric solution to the problem of finding singularity-free paths joining two arbitrary points in the constant orientation workspace of a semi-regular Stewart platform manipulator. The formulation builds upon the known closed-form expression for the gain-type singularity surface of the manipulator. Using a rational parametrisation of the surface, it computes the geodesic curve on this surface, connecting the projections of the two given points on this surface. A sequence of spheres is then constructed in such a manner that each sphere is tangential to a previous one as well as the singularity surface, at a point on the said geodesic curve. Thus the geodesic curve acts as a guide, over which the singularity-free sphere is rolled, till it reaches its destination. Multiple methods for computing such sequences of spheres are presented and compared with the help of a numerical example. Finally, a sequence of line segments connecting the centres of the spheres is constructed, which connects the two given points via a provably singularity-free path.