A geometrical setting for the newtonian mechanics of robots

Reuven Segev (1) , Amit Ailon (2)

1 Department of Mechanical Engineering [Beer-Sheva]
2 Department of Electrical and Computer Engineering [Beer-Sheva]

A geometrical setting for the Newtonian mechanics of mechanical manipulators is presented. The configuration space of the mechanical system is modelled by a differentiable manifold. The kinematics of the system is formulated on the tangent and double tangent bundles of the configuration space, and forces are defined as elements of the cotangent bundle. The dynamical properties of the system are introduced by specifying a Riemannian metric on the configuration space. The metric is used in order to generate the generalized momenta and the kinetic energy from the generalized velocities, and the connection it induces makes it possible to formulate a generalization of Newton's second law relating generalized forces and generalized accelerations.

Domaines: Mécanique [physics.med-ph]

Reuven Segev, Amit Ailon. A geometrical setting for the newtonian mechanics of robots. Journal of The Franklin Institute, 1986, 322 (3), pp.173-183. ⟨hal-00956482⟩