Sandipan Bandyopadhyay

Determination of the Safe Working Zone of a Parallel Manipulator

This paper formalises the concept of safe working zone (SWZ) of a parallel manipulator, which is a subspace of the workspace that is free of singularities as well as issues of joint limits and link interference. It presents further a generic scheme to identify such a space, and specialises the same for the case of a convex SWZ around a chosen point of interest. The theoretical developments are illustrated via an application on a three-degree-of-freedom spatial parallel manipulator, namely, MaPaMan-I.

Analysis of Constraint Equations and Their Singularities

The identification of singularities is an important aspect of research in parallel manipulators, which has received a great deal of attention in the past few decades. Yet, even in many well-studied manipulators, very few reported results are of complete or analytical nature. This chapter tries to address this issue from a slightly different perspective than the standard method of Jacobian analysis. Using the condition for existence of repeated roots of the univariate equation representing the forward kinematic problem of the manipulator, it shows that it is possible to gain some more analytical insight into such problems. The proposed notions are illustrated by means of applications to a spatial \(3\)-RPS manipulator, leading to the closed-form expressions for the singularity manifold of the \(3\)-RPS in the actuator space.

A new approach towards the synthesis of six-bar double dwell mechanisms

This paper presents a new formulation for the synthesis of planar six-bar linkages with only rotary joints showing two dwells in each cycle of the input crank. The formulation combines the concepts of instantaneous kinematics and optimisation to produce a simple, one-step synthesis method. The method is illustrated with a numerical example, where it is seen to produce better results in terms of accuracy and computational efficiency with respect to reported works.

Position Kinematics of a 3-RRS Parallel Manipulator

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 16\(^{th}\) 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.

Singular Manifold of the General Hexagonal Stewart Platform Manipulator

The knowledge of the singular manifold of a manipulator is essential for its design, path-planning and control. However, due to the computational complexity, it is very difficult to obtain an analytical description of the manifold in terms of the architecture as well as configuration parameters of the manipulator. In this paper, the singularity of a general hexagonal Stewart platform manipulator (GHSPM) is studied and its singular manifold is obtained. The manifolds geometric structure is analysed by projecting it to the position and orientation subspaces, respectively. An explicit geometric characterisation is obtained in the former case, where is it found that the geometric nature of the singular surface is the same as in the case of the SRSPM. The other surface, however, defies such analysis at this point due to its high degree. The theoretical results are illustrated with numerical examples and plots.

Optimisation of double wishbone suspension system using multi-objective genetic algorithm

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 midrange 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.

A Deterministic Attitude Estimation Using a Single Vector Information and Rate Gyros

This paper proposes a deterministic estimator for the estimation of the attitude of a rigid body. A deterministic estimator uses a minimal set of information and does not try to minimize a cost function or lit the measurements into a stochastic process. The proposed estimator obtains the attitude estimation utilizing only the properties of the rotational group SO(3). The information set required by the proposed estimator is a single vector information and rate gyro readings. For systems in which one of the rotational freedom is constrained, the proposed estimator provides an accurate estimate of the reduced attitude. The performance of the algorithm is verilied on different experimental testbeds.

Identifying Singularity-Free Spheres in the Position Workspace of Semi-regular Stewart Platform Manipulators

This paper presents a method to compute the largest sphere inside the position-workspace of a semi-regular Stewart platform manipulator , that is free of gain-type singularities. The sphere is specific to a given orientation of the moving platform, and is centred at a designated point of interest. The computation is performed in two parts; in the first part, a Computer Algebra System (CAS) is used to derive a set of exact symbolic expressions, which are then used further in a purely numerical manner for faster computation. The method thus affords high computation speed, while retaining the exactness and generic nature of the results. The numerical results are validated against those obtained from an established numerical algebraic geometry tool, namely, Bertini, and are illustrated via an example.

A novel characterisation of spatial manipulators based on their degrees-of-freedom

This paper deals with the nature of the degree(s)-of-freedom(DoF) of spatial manipulators. When such manipulators have less than six DoF, it is generally not clear as to how many of its DoF are rotational in nature and how many purely translational. The problem is further complicated by the fact that the split of the total DoF in these categories can change for the same manipulator at different subsets of its configuration space. This paper elaborates the concept of partitioning of DoF introduced in [1] and uses it to present a classification of spatial manipulators based on the nature of its motion at any given configuration. The identification of these classes in terms of the configuration and architecture of the manipulators can help substantially in their design. The impact of some changes of architecture on the instantaneous DoF of a 3-RPS spatial manipulator is presented to illustrate the theory developed in the paper.

A Comparative Study of the Configuration-Space and Actuator-Space Forward Dynamics of Closed-Loop Mechanisms Using the Lagrangian Formalism

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.