Multibody system is the study of the dynamic behavior of interconnected rigid or flexible bodies, each of which may undergo large translational and rotational displacements.
The systematic treatment of the dynamic behavior of interconnected bodies has led to a large number of important multibody formalisms in the field of mechanics.
The dynamic behavior results from the equilibrium of applied forces and the rate of change of momentum.
Nowadays, the term multibody system is related to a large number of engineering fields of research, especially in robotics and vehicle dynamics.
As an important feature, multibody system formalisms usually offer an algorithmic, computer-aided way to model, analyze, simulate and optimize the arbitrary motion of possibly thousands of interconnected bodies.
The sliding mass is not allowed to rotate and three revolute joints are used to connect the bodies.
An example of a body is the arm of a robot, a wheel or axle in a car or the human forearm.
The link is defined by certain (kinematical) constraints that restrict the relative motion of the bodies.
The degrees of freedom denote the number of independent kinematical possibilities to move.
In other words, degrees of freedom are the minimum number of parameters required to completely define the position of an entity in space.
The degrees of freedom in planar motion can be easily demonstrated using a computer mouse.
A constraint condition implies a restriction in the kinematical degrees of freedom of one or more bodies.
The classical constraint is usually an algebraic equation that defines the relative translation or rotation between two bodies.
Each multibody system formulation may lead to a different mathematical appearance of the equations of motion while the physics behind is the same.
The motion of the constrained bodies is described by means of equations that result basically from Newton’s second law.
The equations are written for general motion of the single bodies with the addition of constraint conditions.
includes quadratic terms of velocities and it results due to partial derivatives of the kinetic energy of the body.
The Lagrange multipliers do no "work" as compared to external forces that change the potential energy of a body.
Several algorithms have been developed for the derivation of minimal coordinate equations of motion, to mention only the so-called recursive formulation.
While the reduced system might be solved more efficiently, the transformation of the coordinates might be computationally expensive.
For example in cases where flexibility plays a fundamental role in kinematics as well as in compliant mechanisms.