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Multibody Dynamics

Apply and sense force, torque, and motion

Multibody dynamics is the study of the dynamic behaviors of mechanical systems that consist of rigid and/or flexible bodies connected by joints. The bodies undergo translational and rotational motions caused by applied forces, torques, and constraints. Simscape™ Multibody™ enables you to perform multibody dynamics simulations for complex systems, such as robots, vehicles, construction equipment, or aircraft landing gear. You can specify force, torque, and motion inputs to drive your model and simulate the dynamic responses of the model.

To specify the degrees of freedom between a pair of bodies, use blocks in the Joints and Constraints libraries. For example, you can use the Prismatic Joint block and Revolute Joint block to model the straight-line and rotary motions of a slider-crank mechanism. You can use the Point on Curve Constraint block to model the constraint between a roller coaster car and the track.

To model forces and torques that act on bodies, use blocks in the Forces and Torques library. For example, you can use the Magic Formula Tire Force and Torque block to model the tire forces and torques between a tire and ground surface. When modeling contact problems, such as robotic grasping, you can use the Spatial Contact Force block to simulate forces between a pair of bodies.

To measure the relative motions between bodies, you can use the Transform Sensor block. To measure forces and torques, you can use blocks in the Constraints, Joints, and Forces and Torques libraries. The loads on the bodies at the joints can be measured at the joint blocks, and a constraint block can sense the forces and torques that maintain the constraint between a pair of bodies. Each of these quantities help you answer important questions as you analyze the multibody dynamics of the mechanical system.


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simscape.multibody.AxialSpringDamperConstruct axial spring-damper force law
simscape.multibody.JointForceLawAbstract base class to construct joint force laws
simscape.multibody.SphericalSpringDamperConstruct spherical spring-damper force law
simscape.multibody.TorsionalSpringDamperConstruct torsional spring-damper force law

Simscape Blocks

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Angle ConstraintFixed angle between two frame Z axes
Distance ConstraintFixed distance between two frame origins
Point on Curve ConstraintKinematic constraint between frame origin and curved path
Point on Surface ConstraintKinematic constraint between frame origin and 2-D surface

Joints with One or No Primitives

Prismatic JointJoint with one prismatic primitive
Revolute JointJoint with one revolute primitive
Spherical JointJoint with one spherical primitive
Weld JointJoint with zero primitives

Joints with Multiple Primitives

Bearing JointJoint with one prismatic and three revolute primitives
Bushing JointJoint with three prismatic and three revolute primitives
Cartesian JointJoint with three prismatic primitives
Cylindrical JointJoint with one prismatic and one revolute primitives possessing parallel motion axes
Gimbal JointJoint with three revolute primitives
Pin Slot JointJoint with one prismatic and one revolute primitives possessing mutually orthogonal motion axes
Planar JointJoint with one revolute and two prismatic primitives
Rectangular JointJoint with two prismatic primitives
6-DOF JointJoint with one spherical and three prismatic primitives
Telescoping JointJoint with one prismatic and one spherical joint primitive
Universal JointJoint with two revolute primitives

Joints with Coupled Degrees of Freedom

Constant Velocity JointJoint that enforces a constant-velocity kinematic constraint between two shafts
Lead Screw JointJoint with coupled rotational and translational degrees of freedom
External Force and TorqueGeneral force and torque arising outside the modeled system
Gravitational FieldField of force due to point mass
Internal ForceGeneral force acting reciprocally between two frame origins
Inverse Square Law ForceForce proportional to the inverse square distance between two frame origins
Magic Formula Tire Force and TorqueApply steady-state tire force and torque by using Magic Formula tire equations
Spatial Contact ForceModel contact between two geometries
Spring and Damper ForceForce proportional to the distance and relative velocity between two frame origins
Transform SensorSensor that measures the relative spatial relationship between two frames
Mechanism ConfigurationMechanism-wide simulation and mechanical parameters


Sense Force, Torque, and Motion Outputs

Prescribe Force, Torque, and Motion Inputs

Force and Torque Specification

Motion, Force, and Torque Sensing