Constraints in Multibody Systems

The formulation of the equations of motion for large multibody systems requires systematic formulations of the constraints at the joints. Due to the lesser importance of nonholonomic constraints in the modeling of technical systems, joints with holonomic constraints are considered. The couplings of the bodies through joints determine the topological structure as an open multibody system with tree structure or as a partially or fully closed multibody system with kinematic loops. Depending on the motions of the bodies, planar, spherical and spatial multibody systems can be distinguished. If all constraints are independent of each other, the degree of freedom of the multibody system can be determined using the Grübler-Kutzbach criterion. The holonomic constraints at joints are formulated vectorially using implicit and explicit representations. The explicit and implicit constraint reaction conditions apply to the constraint wrenches at the joints. A concluding overview shows the use of joint constraints in the different formulations of the equations of motion of multibody systems.