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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.JointActuationDictionaryDictionary to store joint primitive actuations (Since R2024a)
simscape.multibody.PrismaticPrimitiveActuationForceConstruct actuation force for prismatic joint primitive (Since R2024a)
simscape.multibody.RevolutePrimitiveActuationTorqueConstruct actuation torque for revolute joint primitive (Since R2024a)
simscape.multibody.SphericalPrimitiveActuationTorqueConstruct actuation torque for spherical joint primitive (Since R2024a)
simscape.multibody.AxialSpringDamperConstruct axial spring-damper force law (Since R2022a)
simscape.multibody.JointForceLawAbstract base class to construct joint force laws (Since R2022a)
simscape.multibody.SphericalSpringDamperConstruct spherical spring-damper force law (Since R2022a)
simscape.multibody.TorsionalSpringDamperConstruct torsional spring-damper force law (Since R2022a)

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 (Since R2021a)

Joints with One or No Primitives

Prismatic JointJoint that allows relative motion along single axis
Revolute JointJoint with one revolute primitive
Spherical JointJoint allows 3-D rotations
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 rotational and one translational degree of freedom
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 rotational and two translational degrees of freedom
Rectangular JointJoint with two prismatic primitives
6-DOF JointJoint with six degrees of freedom and no kinematic singularity
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
Custom Tire Force and TorqueCompute interactions and spatial relationships between tire and ground surface (Since R2024a)
External Force and TorqueApply external force and/or torque to connected frame
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 (Since R2021b)
Planar Contact ForceModel planar contact between two geometries (Since R2023b)
Spatial Contact ForceModel spatial contact between two geometries (Since R2019b)
Spring and Damper ForceForce proportional to the distance and relative velocity between two frame origins
Inertia SensorSensor to measure the inertial properties of body groups or mechanisms (Since R2019b)
Transform SensorSensor that measures the relative spatial relationship between two frames
Mechanism ConfigurationMechanism-wide gravity and simulation parameters


Sense Force, Torque, and Motion Outputs

Prescribe Force, Torque, and Motion Inputs

Force and Torque Specification

Motion, Force, and Torque Sensing