This paper studies the configuration-space and the actuator-space variants of the Lagrangian formulation of dynamics of parallel manipulators. In particular, the effects of the gain-type singularity and the configuration-space singularity on the forward and inverse dynamic analyses using these formulations are studied in detail. A condition for kinematic consistency at a gain-type singularity is established. The formulations are implemented on a planar five-bar manipulator and a bi-planar Stewart platform manipulator. Extensive numerical simulations augment the analytical developments in the understanding of the dynamic behaviour of the manipulators, in both the singular and the non-singular cases. © 2018 Elsevier Ltd

Sandipan Bandyopadhyay

Department of Engineering Design

Actuators

Dynamics

KINEMATICS

Lagrange multipliers

Wave functions

Configuration space

FORWARD AND INVERSE DYNAMICS

GAIN-TYPE SINGULARITIES

KINEMATIC SINGULARITY

Lagrangian dynamics

LAGRANGIAN FORMULATIONS

Parallel manipulators

STEWART PLATFORM MANIPULATOR

Manipulators

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Mechanism and Machine Theory

Two optimal design methods are proposed for the dimensional design of parallel manipulators, considering their dynamic performance over the desired ranges of motions, velocities, and accelerations. The first method, termed as the extrinsic method, directly minimises the actuator forces/torques within the desired safe working zone of the manipulator, for typical velocities and accelerations of the end-effector. The second method, namely, the intrinsic method, minimises a measure of the manipulator's inertia, as reflected at the actuators, over the said safe working zone. Case studies on the design of 3-RRR and 3-RRS manipulators are presented to illustrate the proposed methods. Numerical studies show that the optimal link dimensions obtained through these conceptually disparate methods are fairly similar. Naturally, the dynamic performances of the resulting manipulators are also comparable, which are found to be significantly better than that of arbitrary designs respecting the same constraints. © 2019 Elsevier Ltd

Methods for dimensional design of parallel manipulators for optimal dynamic performance over a given safe working zone

This paper proposes a control scheme that allows parallel manipulators to overcome a major inherent challenge, namely, avoiding singularities occurring inside their workspaces. The scheme lets a parallel manipulator follow a path that originally contains such singularities. By means of a suitably chosen artificial potential function arising out of the proximity to the singularities, the behaviour of the manipulator is modified dynamically, enabling it to push away the singularities in its path, without deviating from the path itself. Such behaviour is obtained, however, at the cost of one of the DoF of the manipulator. Nevertheless, various application scenarios involving axi-symmetric tools, e.g., industrial operations such as welding and gas cutting, can afford such a trade-off, and thereby benefit by eliminating the requirement of checking each path for singularities a priori. An additional benefit is the increase in the effective size of the workspaces due to the avoidance of internal singularities. The theory developed is applicable to any parallel manipulator, in principle. In this paper, it has been applied to a three- DoF planar 3-RRR manipulator. The experimental results clearly demonstrate the efficacy of the proposed scheme. © 2015 Elsevier Ltd. All rights reserved.

Dynamic singularity avoidance for parallel manipulators using a task-priority based control scheme

In this work, a reduced-order forward dynamics of multiclosed-loop systems is proposed by exploiting the associated inherent kinematic constraints at acceleration level. First, a closed-loop system is divided into an equivalent open architecture consisting of several serial and tree-type subsystems by introducing cuts at appropriate joints. The resulting cut joints are replaced by appropriate constraint forces also referred to as Lagrange multipliers. Next, for each subsystem, the governing equations of motion are derived in terms of the Lagrange multipliers, which are based on the Newton-Euler formulation coupled with the concept of Decoupled Natural Orthogonal Complement (DeNOC) matrices, introduced elsewhere. In the proposed forward dynamics formulation, Lagrange multipliers are calculated sequentially at the subsystem level, and later treated as external forces to the resulting serial or tree-type systems of the original closed-loop system, for the recursive computation of joint accelerations. Note that such subsystem-level treatment allows one to use already existing algorithms for serial and tree-type systems. Hence, one can perform the dynamic analyses relatively quickly without rewriting the complete model of the closed-loop system at hand. The proposed methodology is in contrast to the conventional approaches, where the Lagrange multipliers are calculated together at the system level or simultaneously along with the joint accelerations, both of which incur higher order computational complexities, and thereby a greater number of arithmetic operations. Due to the smaller size of matrices involved in evaluating Lagrange multipliers in the proposed methodology, and the recursive computation of the joint accelerations, the overall numerical performances like computational efficiency, etc,; are likely to improve. The proposed reduced-order forward dynamics formulation is illustrated with two multiclosed-loop systems, namely, a 7-bar carpet scrapping mechanism and a 3-RRR parallel manipulator. © 2013 Springer Science+Business Media Dordrecht.

Multibody System Dynamics

Reduced-order forward dynamics of multiclosed-loop systems

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. © Springer Science+Business Media Dordrecht 2012.

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Journal	Data powered by TypesetMechanism and Machine Theory
Publisher	Data powered by TypesetElsevier Ltd
ISSN	0094114X
Open Access	No