The efficient implementation of kinematics and dynamics models is a key to model based control of mechatronic systems such as robots and wearable assistive devices. This paper presents an approach for the derivation of these models in symbolic form for constrained systems based on the explicit elimination of the kinematic constraints using substitution variables with trigonometric expressions and the Lagrange equations of the second kind. This represents an alternative solution to using the implicit form of the constraints or using the explicit elimination at comparable computational effort. The method is applied to a novel exoskeleton designed for craftsmen force assistance, which consists of multiple planar closed kinematic loops and gear mechanisms.