In this research, the dynamics equations for a demolition fire vehicle were formulated. This was done by developing an interface that allows co-simulation using ADAMS and MATHEMATICA. In this study, MATHEMATICA alone was used to calculate the constrained dynamics equations, to demonstrate the impact force and the constraint Jacobian of the end-effector as any desired location through the x, y and z axes. Then we mathematically derived a model for a unilaterally constrained multi-link. Assumptions about the fire demolition vehicle of the constraint coordinate and the impact issues of the model are discussed in the next sections. The estimation procedure for the dynamics equation showed good approximation results in terms of solving a reaching task problem.