Velocity and Acceleration Analyses of Lower Mobility Platforms via Screw Theory

2016

Meccanica

The mobility analysis of mechanisms rests on an adequate formulation of the constraints defining its configuration space (c-space). Whereas there is no general method for a global analysis, the higher-order mobility analysis, which locally approximates the c-space, is applicable to general mechanisms. It requires an efficient method for the evaluation of higher-order constraints, i.e. constraints on velocity, acceleration, jerk, etc. Such a method is known for linkages comprising lower pair joints only. In this paper a method for the efficient evaluation of higherorder constraints for mechanisms comprising higher pair joints is proposed. The method builds on the results for the lower pair linkages. It leads to a computationally simply recursive algorithm. This is applied to the mobility analysis that allows to determine the local finite mobility, to detect singularities, and to identify shaky mechanisms.

Section: Cut-joint Versus Cut-body Formulationmentioning

confidence: 99%

“…This gives rise to explicit algebraic relations of the derivatives of the kinematic mapping, and hence of the derivatives of the loop closure constraints for lower pair linkages. These higher-order constraints were employed to the mobility analysis of lower pair linkages [5,6,11,18,20,22].…”

mentioning

confidence: 99%

Higher-order constraints for higher kinematic pairs and their application to mobility and shakiness analysis of mechanisms

2016

Meccanica

“…Furthermore, this provides the basis for higher-order kinematic analysis of mechanisms. This has been pursued in Rico et al (1999Rico et al ( , 2008 and Müller and Rico (2008) for single-loop mechanisms. The extension to multi-loop mechanisms requires a systematic yet simple description of the mechanism topology.…”

Section: Mechanism Configurationmentioning

confidence: 99%

Representation of the kinematic topology of mechanisms for kinematic analysis

2015

Mech. Sci.

Abstract. The kinematic modeling of multi-loop mechanisms requires a systematic representation of the kinematic topology, i.e. the arrangement of links and joints. A linear graph, called the topological graph, is used to this end. Various forms of this graph have been introduced for application in mechanism kinematics and multibody dynamics aiming at matrix formulations of the governing equations. For the (higher-order) kinematic analysis of mechanisms a simple yet stringent representation of the topological information is often sufficient. This paper proposes a simple concept and notation for use in kinematic analysis. Upon a topological graph, an order relation of links and joints is introduced allowing for recursive computation of the mechanism configuration. An ordering is also introduced on the topologically independent fundamental cycles. The latter is indispensable for formulating generically independent loop closure constraints. These are presented for linkages with only lower pairs, as well as for mechanisms with one higher kinematic pair per fundamental cycle. The corresponding formulation is known as cut-body and cut-joint approach, respectively.

Closed Form Expressions for Higher Derivatives of Screw Systems

Volume 6B: 37th Mechanisms and Robotics Conference

2013

A central element in the kinematic analysis is the determination of partial derivatives of the twist of a member in a serial kinematic chain with respect to the joint parameters (angles, translations). This requires partial derivatives of the screw system, generated by a given ordered set of joint screws. While the closed form expression of first and second order derivatives are widely known in terms of screw products, and even the derivatives up to fifth order have been reported, a general closed form expression for derivatives of arbitrary order remained an open issue. Such a closed form expression of partial derivatives of the joint screws for any order is reported in this paper. The final result for the n-th partial derivative involves n-fold nested Lie bracket (screw products) of the joint screws. The crucial observation that gives rise to the closed form expression is that the derivative is given as a sum of terms with complementary joint index ranges.