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In this article we derive the equations of motion of a kinematic chain using concepts naturally associated with the special euclidean group. A simple and coordinate-free formula for the kinetic energy of a rigid body is used to express the kinetic energy of an open chain. From this, the dynamical equations in the Lagrangian form follow easily. The structure of the equations of motion is sufficiently transparent so that one may gain insight into nontrivial problems involving analysis and design. We illustrate the applicability of this formalism by investigating the design of manipulators with configuration- independent and separable kinetic energy.