Energy-momentum conserving integration of parallel manipulators

In the framework of a rotationless formulation for multibody systems, we present an investigation of multibody mechanisms. The benefit of this kind of formulation is the design of energy-momentum conserving integration schemes, which facilitate a stable numerical integration of differential algebraic equations governing the motion of open-loop and closed-loop systems. We introduce a coordinate augmenation technique for the incorporation of rotational degrees of freedom and subsequently perform a size-reduction to lower the computational costs and to improve the numerical conditioning [1]. Furthermore the treatment of nonholonomic constraints is addressed [3]. Copyright line will be provided by the publisher 1 Equations of motion The underlying set of equations of motion is of DAE-type due to the usage of redundant coordinates for the rigid body kinematics. For holonomic scleronomic constraints we obtain: q ̇ − v = 0 Mv ̇ − f (q) +GT (q)λ = 0 φ(q) = 0 2n+m equations with q ∈ Rn being the configurational vector, λ ∈ Rm the Lagrange multipliers and φ ∈ Rm the vector of constraints. The design of a mechanical time integrator is based on the direct discretization of the DAEs. In addition to that the notion of a discrete derivative, introduced by Gonzalez [2] (red marked terms), is applied. The discretized set of equations leads to the Basic Energy-Momentum scheme [1]: qn+1 − qn