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

expand all

Joint Actuations

`simscape.multibody.JointActuationDictionary`	Dictionary to store joint primitive actuations (Since R2024a)
`simscape.multibody.PrismaticPrimitiveActuationForce`	Construct actuation force for prismatic joint primitive (Since R2024a)
`simscape.multibody.RevolutePrimitiveActuationTorque`	Construct actuation torque for revolute joint primitive (Since R2024a)
`simscape.multibody.SphericalPrimitiveActuationTorque`	Construct actuation torque for spherical joint primitive (Since R2024a)

Joint Force Laws

`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

expand all

Constraints

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

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 orthogonal prismatic and revolute primitives
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 spherical and one prismatic joint primitive
Universal Joint	Joint that allows for transfer of rotary motion between unaligned shafts

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

Loads

Custom Tire Force and Torque	Compute interactions and spatial relationships between tire and ground surface (Since R2024a)
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
Spring and Damper Force	Force proportional to the distance and relative velocity between two frame origins

Sensors

Inertia Sensor	Sensor to measure the inertial properties of body groups or mechanisms
Transform Sensor	Sensor that measures the relative spatial relationship between two frames

Utilities

Mechanism Configuration

Mechanism-wide gravity and simulation parameters

Topics

Sense Force, Torque, and Motion Outputs

Analyze Motion at Various Parameter Values
Simulate a four-bar model at different coupler link lengths and plot the resulting coupler curves.
Sensing
Dynamic variables that you can sense and blocks that you can use to sense them.
Sense Motion Using a Transform Sensor Block
Use the Transform Sensor block to sense frame motion in a simple multibody model.
Measure Joint Constraint Forces
Use the sensing capability of a joint block to sense the internal forces acting on a mechanical link.
Measure Forces and Torques Acting at Joints
Use the sensing capability of joint blocks to measure the forces and torques acting at a joint.

Prescribe Force, Torque, and Motion Inputs

Modeling Contact Force Between Two Solids
Use the Spatial Contact Force block to model normal and frictional forces between solid blocks.
Solid Cylinder Rolling Down an Incline
Use the Spatial Contact Force block to model the solid cylinder rolling down a ramp.
Model Gravity in a Planetary System
Assemble a system of gravitationally-bound free bodies using Cartesian Joint and Gravitational Field blocks.
Specify Joint Motion in Planar Manipulator Model
Use the actuation capability of joint blocks to specify the trajectory of frame.
Specify Joint Actuation Torque
Use the actuation capability of a joint block to specify the actuation torque on a joint.
Specify Joint Motion Profile
Use the actuation capability of joint blocks to specify the trajectory of a frame.
Use Contact Proxies to Simulate Contact
Use contact proxies to increase the speed and robustness of contact simulations.

Force and Torque Specification

Actuating and Sensing with Physical Signals
Using physical signals to specify actuation inputs and obtain sensing outputs.
Joint Actuation Limitations
Restrictions and special considerations for models with motion actuation inputs in joint blocks.
Modeling and Measuring System Dynamics
Workflow steps for setting and sensing dynamic quantities such as force, torque, position, and more.
Modeling Gravity
Modeling the effects of uniform gravity, gravitational fields, and individual gravitational forces. Software definition of body boundaries and its impact on gravitational torques.
Specifying Joint Actuation Inputs
Joint actuation modes, motion input handling, and key differences between model assembly and simulation.

Motion, Force, and Torque Sensing

Force and Torque Sensing
Forces and torques that you can sense and the blocks that you can use to sense them.
Selecting a Measurement Frame
Measurement frame definition and summary of measurement frame types.
Motion Sensing
Motion variables that you can sense and the blocks that you can use to sense them.
Rotational Measurements
Rotational motion variables that you can sense and the blocks that you can use to sense them.
Translational Measurements
Translational variables that you can sense and the blocks that you can use to sense them.

Featured Examples

Backhoe

Model a hydraulically actuated backhoe with closed-loop PID control.

Open Model

Computing Actuator Torques Using Inverse Dynamics

Illustrates the use of motion actuation to determine the actuator torques needed for the robot to achieve a given welding task. The system consists of a seven degree of freedom robot carrying a welding torch. The tip of the torch needs to trace the joints being welded. In this example the tip of the torch is made to trace (using motion actuation) a plus sign, a circle and a star sign on the workpiece. The torch is lifted off the workpiece when transitioning between the different shapes. The motion of the welding torch is specified and the actuator torques required at the various joints of the robot to achieve this motion is computed.

Open Model

Contact Modeling - Ball on Grid Surface

A ball and dumbbell rolling down on an L-shaped surface. Grid Surface block is used to generate the L-shaped membrane. Point Cloud blocks are used to model the contact between the ball/dumbbell and the surface. The number of point blocks can be controlled by varying the point cloud density. This example demonstrates the capabilities of Grid Surface and Point Cloud blocks to model contacts between complex shaped bodies.

Open Model

Hydraulic Interface - Dump Trailer with Hydraulic Cylinder

A dump trailer powered by a double-acting hydraulic cylinder. The cylinder actuates a scissor hoist mechanism that raises and lowers the dump bed. The model provides an example of how to interface Simscape™ Multibody™ joints with Simscape components that have mechanical domain ports.

Open Model

Inverted Double Pendulum on a Sliding Cart

Model an inverted double pendulum mounted on a sliding cart using Simscape™ Multibody™. It also illustrates the use of a controller to balance the pendulum in the upright position. Make any changes to the system and click on the blue box to generate a linearized model for the system before running the simulation. The control gains are computed using the linearized model. The pole placement technique is used to compute the control gains from the linearized model. The controller keeps the double pendulum vertical in the presence of a random disturbance force. See the supporting files linearize.m and controlGains.m for details.

Open Model

Lead Screw with Friction

Models a lead screw with friction. The constraint force in the lead screw is measured and used to calculate the friction torque within the lead screw. A continuous stick-slip friction model is used to determine the coefficient of friction based on the relative rotational speed of the two parts connected by the lead screw.

Open Model

Measure Inertial Properties of Multibody Systems

Measure the inertial properties, such as mass and center of mass, of a group of bodies or an entire mechanism by using the Inertia Sensor block.

Open Live Script

Modeling Self-Locking Worm and Gear Constraints - Worm Jack

Models a self-locking worm and gear constraint. The model shows a mechanical jack driven by a torque applied to a worm. The model includes two worm jack subsystems identical in every sense except for the value of the worm lead angle. Both subsystems have friction models applied to their Worm and Gear Constraint blocks.

Open Model

Ratchet Pawl Mechanism

Models a ratchet with a locking pawl. The arm pushes the driving pawl to rotate the ratchet wheel. The locking pawl holds the ratchet wheel in place while the arm reverses direction. Planar contact modeling geometry is used to streamline computation.

Open Model

Ratchet Lifter

Models a ratchet lifter and demonstrates how to use contact proxies for contact problems that involve complex geometries.

Open Model

Rotational Interface: Electrically Operated Bread Slicer

This model simulates an electrically operated 1-DOF bread slicing mechanism. The electrical circuit and motor are modeled in Simscape™ while the bread slicing mechanism is modeled in Simscape Multibody™. The model uses a Rotational Multibody Interface block to connect the Simscape components to a Revolute Joint block in Multibody.

Open Model

Sensing Composite Forces and Torques in Joints - Potter's Wheel

The example shows how you can sense forces and torques acting at joints. A potter's wheel spins with a piecewise linear velocity profile while holding a piece of clay off center. The clay creates a dynamic imbalance, generating periodic constraint forces at the joints. Viscous damping accounts for energy dissipation in the axle.

Open Model

Translational Interface: Radial Engine with Gas Force Model

This model simulates a five cylinder radial engine. The pressure dynamics inside the cylinders are modelled using the Simscape™ Foundation Library gas and mechanical translational domains. The 3D mechanical components are modelled using Simscape Multibody™. See inside any of the blocks called "Force Model" to see how the 1D Simscape and 3D Multibody parts of the model are interfaced. The pressure model is an ideal pressure source which applies pressure based on the crank angle. This model can be replaced with a more realistic pressure model of the cylinder chamber. The cylinders fire in the sequence - A C E B D providing a power stroke every 144 deg of crank rotation.

Open Model

Using the Spatial Contact Force Block - Bumper Car

A toy bumper car traveling down a series of ramps while undergoing intermittent collisions. Spatial Contact Force blocks are used to model the friction and normal forces between every pair of geometries that may potentially come into contact during the simulation (e.g., between one of the car's wheels and a railing). Each Spatial Contact Force block is able to generate brief high-impact contact forces to model collisions, as well as sustained contact forces to model rolling and sliding.

Open Model