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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.

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 ForceApply contact forces between a pair of connected bodies
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

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.

Sense Constraint Forces

Use the sensing capability of a joint block to sense the internal forces acting on a mechanical link.

Sense 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.

Model Wheel Contact in a Car

Use the Spatial Contact Force block to model the wheels of a car 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.

Prescribe 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 Sensing 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