Mehrkörpersystems

Mehrkörpersystems, or multibody systems, describe assemblies of rigid or flexible bodies connected by joints and constraints whose relative motion is restricted. They are used to analyze the motion, forces, and control of mechanical systems ranging from robots and vehicles to biomechanical models.

The standard modeling framework uses classical mechanics, typically Newton-Euler or Lagrangian formalisms. Generalized coordinates q capture the positions and orientations of each body, while constraint equations Phi(q,t)=0 enforce joints and connections. The resulting equations of motion are often expressed as a system of differential-algebraic equations (DAEs), for example in a form that includes mass matrices M(q), Coriolis terms, and constraint multipliers lambda to enforce Phi. Joints such as revolute, prismatic, spherical, cylindrical and universal define linkage topologies and introduce holonomic or nonholonomic constraints, which distinguish purely positional restrictions from velocity-based ones.

Models can assume rigid bodies for simplicity, or incorporate flexible components through reduced-order representations or floating-frame methods. Additional elements include actuators, sensors, contact models, and friction. Simulation typically involves selecting coordinates, deriving equations, setting initial conditions, and integrating over time to obtain trajectories and reaction forces. Challenges include numerical stiffness, constraint drift, and accurately representing contact and friction.

Software tools for Mehrkörpersystems encompass specialized libraries and simulation environments that support multibody dynamics, such as Simbody, Chrono, OpenSim, and MATLAB/Simulink with Simscape Multibody. Applications span robotics design and control, automotive suspension and drivetrain analysis, aerospace mechanisms, and gait or prosthetic modeling in biomechanics. The field emphasizes modular modeling, scalable computation, and integration with control systems and optimization workflows.