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Journals and Conferences
In this lecture the group of rigid body motions is introduced via its representation on standard three dimensional Euclidian space. The relevance for robotics is that the links of a robot are usually modelled as rigid bodies. Moreover the payload of a robot is also usually a rigid body and hence much of robotics is concerned with understanding rigid… (More)
In this work we construct a simple dynamical model for vibratory bowl feeders. The symmetrical arrangement of the springs supporting the bowl allow us to predict a simple structure for the stiffness matrix of the system. The cylindrical symmetry of the bowl itself then means that the linearized rigid body dynamics of the system can be simplified to a… (More)
Three rather different problems in robotics are studied using the same technique from screw theory. The first problem concerns systems of springs. We differentiate the potential function in the direction of an arbitrary screw to find the equilibrium position. The second problem is almost identical in terms of the computations, we seek the least squares… (More)
—The Cayley map for the rotation group SO(3) is extended to a map from the Lie algebra of the group of rigid body motions SE(3) to the group itself. This is done in several inequivalent ways. A close connection between these maps and linear line complexes associated with a finite screw motions is found.
This work looks at the stiffness matrix of some simple but very general systems of springs supporting a rigid body. The stiffness matrix is found by symbolically differentiating the potential function. After a short example attention turns to the general structure of the stiffness matrix and in particular the principal screws introduced by Ball.
In this article we derive the deflection equation of a simple beam using screw theory. The effects of tension, torsion and bending of the beam can be unified into a single equation. We begin by looking at the compliance matrix for small elements of the beam. This is loosely based on work by von Mises in the 1920s. We reproduce von Mises results for the… (More)