An Alternative Approach For Teaching Multibody Dynamics

The paper presents an alternative method, the Implicit Constraint Approach (ICA), for developing the equations of motion to describe a system of connected bodies typified by mechanisms and robotic devices. By its simplicity of description and implementation compared to conventional methods, the ICA engages students more in the physics (rather than the mathematics) of the system under study. The ICA enables the direct formation of all needed equations by using only the dynamic equilibrium conditions (in the Newton or Lagrange form). Unlike current approaches, no auxiliary algebraic constraint equations are required. Thus the descriptive equations are ordinary differential equation (ODEs) rather than differential-algebraic equations (DAEs). This leads to simpler mathematics and a broader range of potentially useful numerical integration methods. Examples are provided which illustrate the use of the ICA. The more involved examples employ a general purpose computer program that uses the ICA to provide the kinematics and forces for a planar mechanism of arbitrary complexity.