# 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 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

#### Joints with One or No Primitives

 Prismatic Joint Joint with one prismatic primitive Revolute Joint Joint with one revolute primitive Spherical Joint Joint with one spherical primitive 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 prismatic and one revolute primitives possessing parallel motion axes 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 revolute and two prismatic primitives Rectangular Joint Joint with two prismatic primitives 6-DOF Joint Joint with one spherical and three prismatic primitives 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 General force and torque arising outside the modeled system 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 Spatial Contact Force Apply contact forces between a pair of connected bodies 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 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.