MultiBody

Multibody refers to a mechanical system comprised of multiple interconnected bodies that interact through joints, constraints, and forces. Each body contributes mass and inertia, while connections define the system’s allowable motions. Multibody systems may consist of rigid bodies or include flexible elements, and they are widely used to model mechanisms, vehicles, biological joints, and animated characters.

Key concepts include configuration, constraints, and degrees of freedom. The arrangement of bodies is described by generalized coordinates q. Joints impose kinematic constraints that reduce the independent motions, yielding a system with a finite number of degrees of freedom. Common joint types include revolute (hinge), prismatic (sliding), spherical, cylindrical, universal, and planar joints.

Dynamics of multibody systems can be formulated using Newton-Euler or Lagrangian methods. A typical formulation leads to equations of motion of the form M(q) q̈ + C(q, q̇) q̇ + G(q) = τ + J^T λ, together with constraint equations Φ(q) = 0. Here, M is the mass/inertia matrix, C represents Coriolis and centrifugal terms, G includes potential forces, τ are generalized actuations, J is the constraint Jacobian, and λ are Lagrange multipliers enforcing the constraints. Holonomic constraints depend only on position; nonholonomic constraints depend on velocity.

Applications and methods. Multibody dynamics are simulated numerically, using forward dynamics (given torques, compute motion) or inverse dynamics (compute torques for a prescribed motion). Time integration may be explicit or implicit, and contacts or impacts are often included. Software tools and libraries span commercial packages for engineering design to open-source platforms, and are used in robotics, automotive and aerospace mechanisms, biomechanics, computer animation, and virtual prototyping.

See also: rigid body dynamics, constraint mechanics, Lagrangian mechanics, differential-algebraic equations, multibody simulation.