# 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.

## Classes

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 `simscape.multibody.AxialSpringDamper` Construct axial spring-damper force law (Since R2022a) `simscape.multibody.JointForceLaw` Abstract base class to construct joint force laws (Since R2022a) `simscape.multibody.SphericalSpringDamper` Construct spherical spring-damper force law (Since R2022a) `simscape.multibody.TorsionalSpringDamper` Construct torsional spring-damper force law (Since R2022a)

## Simscape Blocks

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 Angle Constraint Fixed angle between two frame Z axes Distance Constraint Fixed distance between two frame origins Point on Curve Constraint Kinematic constraint between frame origin and curved path Point on Surface Constraint Kinematic constraint between frame origin and 2-D surface (Since R2021a)

#### Joints with One or No Primitives

 Prismatic Joint Joint that allows relative motion along single axis Revolute Joint Joint with one revolute primitive Spherical Joint Joint allows 3-D rotations Weld Joint Joint with zero primitives

#### Joints with Multiple Primitives

 Bearing Joint Joint with one prismatic and three revolute primitives Bushing Joint Joint with three prismatic and three revolute primitives Cartesian Joint Joint with three prismatic primitives Cylindrical Joint Joint with one rotational and one translational degree of freedom Gimbal Joint Joint with three revolute primitives Pin Slot Joint Joint with one prismatic and one revolute primitives possessing mutually orthogonal motion axes Planar Joint Joint with one rotational and two translational degrees of freedom Rectangular Joint Joint with two prismatic primitives 6-DOF Joint Joint with six degrees of freedom and no kinematic singularity Telescoping Joint Joint with one prismatic and one spherical joint primitive Universal Joint Joint with two revolute primitives

#### Joints with Coupled Degrees of Freedom

 Constant Velocity Joint Joint that enforces a constant-velocity kinematic constraint between two shafts Lead Screw Joint Joint with coupled rotational and translational degrees of freedom
 External Force and Torque Apply external force and/or torque to connected frame Gravitational Field Field of force due to point mass Internal Force General force acting reciprocally between two frame origins Inverse Square Law Force Force proportional to the inverse square distance between two frame origins Magic Formula Tire Force and Torque Apply steady-state tire force and torque by using Magic Formula tire equations (Since R2021b) Planar Contact Force Model planar contact between two geometries (Since R2023b) Spatial Contact Force Model spatial contact between two geometries (Since R2019b) Spring and Damper Force Force proportional to the distance and relative velocity between two frame origins
 Transform Sensor Sensor that measures the relative spatial relationship between two frames
 Mechanism Configuration Mechanism-wide gravity and simulation parameters