Geometric constraints and motion branch variations for reconfiguration of single-loop linkages with mobility one

This paper explores essence of geometric constraints induced reconfiguration of single-loop kinematic chains with mobility one. Reconfigurable kinematic chains are firstly classified into four categories in light of variations of parameters in the Chebychev–Grübler–Kutzbach mobility criterion. Within these four categories, single-loop kinematic chains with mobility one but distinct motion branches are further classified in accordance with degeneration of degree-of-freedom of certain revolute joints. With the essence of reconfiguration, the interrelationship of motion-branch changes through constraint singularity induced transitory positions of reconfigurable single-loop linkages is revealed in the context of reciprocity of screws. Four basic geometric constraints leading to transitory positions are explored by analysing the Bennett plano-spherical linkage, a kinematic embodiment of Grassmann varieties. Geometric constraints induced screw-system variation and motion branch changes of a novel asymmetric 7R linkage and the line- and plane-symmetric Bricard 6R linkage with capability of reconfiguring their motion branches are subsequently analysed for interpreting the fundamentals explored

The GR2 gripper: an underactuated hand for open-loop in-hand planar manipulation

Performing dexterous manipulation of unknown objects with robot grippers without using high-fidelity contact sensors, active/sliding surfaces, or a priori workspace exploration is still an open problem in robot manipulation and a necessity for many robotics applications. In this paper, we present a two-fingered gripper topology that enables an enhanced predefined in-hand manipulation primitive controlled without knowing the size, shape, or other particularities of the grasped object. The in-hand manipulation behavior, namely, the planar manipulation of the grasped body, is predefined thanks to a simple hybrid low-level control scheme and has an increased range of motion due to the introduction of an elastic pivot joint between the two fingers. Experimental results with a prototype clearly show the advantages and benefits of the proposed concept. Given the generality of the topology and in-hand manipulation principle, researchers and designers working on multiple areas of robotics can benefit from the findings

A linear relaxation technique for the position analysis of multi-loop linkages

This report presents a new method able to isolate all configurations that a multi-loop linkage can adopt. We tackle the problem by providing formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear and bilinear terms, and trivial trigonometric functions for the helical pair exclusively) whose special structure is later exploited by a branch-and-prune method based on linear relaxations. The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespectively of whether the linkage is rigid or mobile

An Overview of Formulae for the Higher-Order Kinematics of Lower-Pair Chains with Applications in Robotics and Mechanism Theory

The motions of mechanisms can be described in terms of screw coordinates by means of an exponential mapping. The product of exponentials (POE) describes the configuration of a chain of bodies connected by lower pair joints. The kinematics is thus given in terms of joint screws. The POE serves to express loop constraints for mechanisms as well as the forward kinematics of serial manipulators. Besides the compact formulations, the POE gives rise to purely algebraic relations for derivatives wrt. joint variables. It is known that the partial derivatives of the instantaneous joint screws (columns of the geometric Jacobian) are determined by Lie brackets the joint screws. Lesser-known is that derivative of arbitrary order can be compactly expressed by Lie brackets. This has significance for higher-order forward/inverse kinematics and dynamics of robots and multibody systems. Various relations were reported but are scattered in the literature and insufficiently recognized. This paper aims to provide a comprehensive overview of the relevant relations. Its original contributions are closed form and recursive relations for higher-order derivatives and Taylor expansions of various kinematic relations. Their application to kinematic control and dynamics of robotic manipulators and multibody systems is discussed

Multi-loop position analysis via iterated linear programming

Robotics: Science and Systems Conference (RSS), 2006, Filadelfia (EE.UU.)This paper presents a numerical method able to isolate all configurations that an arbitrary loop linkage can adopt, within given ranges for its degrees of freedom. The procedure is general, in the sense that it can be applied to single or multiple intermingled loops of arbitrary topology, and complete, in the sense that all possible solutions get accurately bounded, irrespectively of whether the analyzed linkage is rigid or mobile. The problem is tackled by formulating a system of linear, parabolic, and hyperbolic equations, which is here solved by a new strategy exploiting its structure. The method is conceptually simple, geometric in nature, and easy to implement, yet it provides solutions at the desired accuracy in short computation times.This work was supported by the project 'Planificador de trayectorias para sistemas robotizados de arquitectura arbitraria' (J-00930).Peer Reviewe

The kinematics and vibration of planar linkage mechanisms

PhD ThesisThis thesis reports an investigation into three problems encountered in the design of linkage mechanisms, namely kinematic synthesis, balancing of inertia forces and vibration analysis. A general method of synthesizing planar linkages with pin and sliding joints using an Optimization approach has been investigated. A concise but easily interpreted technique for prescribing the topology of linkages formed by connecting pairs of links together has been developed. The displacement analysis of a linkage is achieved using a direct method which is considerably faster than alternative techniques. A nonlinear optimization algorithm has been modified to cater for non-linear constraints such as transmission angle. These techniques have been incorporated into a computer program. Two case-studies of using the program are given. The first is the synthesis of a six-bar linkage for a motorcycle rear suspension such that a constant centre distance is maintained between the chain-wheels as the suspension deflects. The second concerns the modification of two linkages, containing eight and ten links respectively, to give an improved knitting action for a warp-knitting machine. Operating linkages at high speeds can result in rapidly varying forces acting on the frame due to the mass of the moving links. A procedure to determine suitable counterweights to balance these forces has been developed. Since adding the counterweights may double the total mass of the linkage, the links should have minimum mass. If the mass of a link is reduced too far, the link may vibrate and so detrimentally affect the performance of the linkage. Accordingly the final part reports an investigation into the forced vibration, assuming stability, of a 'Uniform, pin-jointed, binary link. The equations of motion are derived and stability boundaries determined. The theoretical predictions are compared with experimental results from the coupler of a four-bar linkage.Science Research Council: Department of Industry