A geometrical formulation of the dynamical equations describing kinematic chains

A general expression for the kinetic energy associated with a kinematic chain is developed and it is used to derive the dynamical equations. In the authors´ expression for the kinetic energy, the dependence on the chain´s parameters is particularly transparent. Such a representation is desirable in applications such as adaptive control and robot calibration. The kinetic energy is expressed using standard geometric operations, e.g., group multiplication, exponentiation, and adjoint mappings. Lie-theoretic identities are used to simplify the expressions for those derivatives of the inertia matrix which appear in Lagrange´s equations. An elegant expression for the Coriolis terms is provided. The equations of motion for a serial chain are written in a general form which requires no adaptation for specific problems. This representation to classify dynamically balanced chains