Multibody Dynamics Module

Multibody Dynamics Module

Software for Analyzing Assemblies of Rigid and Flexible Bodies

Image made using the COMSOL Multiphysics® software and is provided courtesy of COMSOL.

Analysis of the swashplate mechanism to control orientation of helicopter rotor blades. Transient simulation with both rigid and flexible blade designs provides insight into useful performance metrics such as blade deformation and lift force.

Multibody Dynamics Module

Tools for Designing and Optimizing Multibody Systems

The Multibody Dynamics Module is an expansion of the Structural Mechanics Module that provides an advanced set of tools for designing and optimizing multibody structural mechanics systems using finite element analysis (FEA). The module enables you to simulate mixed systems of flexible and rigid bodies, where each body may be subjected to large rotational or translational displacements. Such analyses help identify critical points in your multibody systems, thus enabling you to perform more detailed component-level structural analyses. The Multibody Dynamics Module also gives you the freedom to analyze forces experienced by segments of the structure, and stresses generated in flexible components that may lead to failure due to large deformation or fatigue.

Utilize a Library of Joints

A library of predefined joints is included in the module so that you can easily and robustly specify the relationships between different components of a multibody system, where the components are interconnected such that only a certain type of motion is allowed between them. Joints connect two components through attachments, where one component moves independently in space while the other is constrained to follow a particular motion, depending on the joint type. The joint types in the Multibody Dynamics Module are generic to the extent that they can model any type of connection. Researchers and engineers can thereby design accurate multibody structural mechanics models, using the following joint types:

  • Prismatic (3D, 2D)
  • Hinge (3D, 2D)
  • Cylindrical (3D)
  • Screw (3D)
  • Planar (3D)
  • Ball (3D)
  • Slot (3D)
  • Reduced Slot (3D, 2D)
  • Fixed Joint (2D,3D)
  • Distance Joint (2D,3D)
  • Universal Joint (3D)

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Product Features

  • Joints can be constrained to restrict the relative motion between the two connected components
  • Joints can be locked to freeze the relative motion between the two connected components at the specified value
  • Spring conditions can be applied on the relative motion at a joint, either at the equilibrium or with pre-deformation
  • Damping or dashpot conditions can be defined to specify losses on the relative motion at a joint
  • Joints can be required to prescribe the relative motion between the connected components
  • Frictional loss to a joint can be added for the joint types: Prismatic, Hinge, Cylindrical, Screw, Planar, and Ball.
  • Forces and moments can be applied to all types of joints at the attachments to the components
  • Mechanisms can be initialized to translate and rotate rigidly with the given velocities about the specified center of rotation

Application Areas

  • Aerospace
  • Automotive
  • Engine dynamics
  • Mechatronics
  • Robotics
  • Biomechanics
  • Biomedical instruments
  • Vehicle dynamics
  • General dynamic simulations of mechanical assemblies


This model illustrates the dynamics of helical gears. It is built using the gears functionality in the Multibody Dynamics interface in COMSOL Multiphysics.

A transient study is performed to analyze the effect of constant gear mesh stiffness, varying gear mesh stiffness, and the transmission error on the angular velocity of driven gear and the contact force. An eigenfrequency analysis is performed to compute the natural frequencies and mode shapes of the gear pair for rigid and for elastic gear mesh.

» See model.

This model simulates the mechanism of a differential gear used in cars and other wheeled vehicles. A differential allows the outer drive wheel to rotate faster than the inner drive wheel during a turn. This is necessary when a vehicle turns in order to allow the wheel that is traveling along the outside of the turning curve to roll faster and to cover greater distance than the wheel on the inside of the turning curve. The average of the rotational speed of the two driving wheels is simply the input rotational speed of the drive shaft. An increase in the speed of one wheel is balanced by a decrease in the speed of the other.

A transient analysis is performed to compute the motion of the spider gears in cases where a vehicle moves on a straight or curved path. The velocity magnitude of the different components and the angular velocity of inner and outer wheels are calculated for the two cases.

» See model.

This model simulates vibrations in a compound gear train. Spur gears, used to model the gear train, are mounted on rigid shafts. The shafts are supported by an elastic housing at both ends. The gear mesh is assumed to be elastic with varying stiffness, which is the source of vibration. A transient analysis is performed to compute the dynamics of the gears as well as the vibrations in the housing.

Contact modeling is used for the computation of the gear mesh stiffness. A parametric analysis is performed to compute the gear mesh stiffness as a function of gear rotation in one mesh cycle.

The model calculates the von Mises stress distribution in the gear pair, where the stresses are high at the contact points, as well as at the roots of the teeth. The gear mesh stiffness, displacement in the gears, and the normal acceleration in the housing due to vibration are also calculated.

» See model.

In this example, a dynamic analysis of a three-cylinder reciprocating engine is performed to investigate stresses generated during operation, thereby permitting identification of the critical components. Demand for high power output relative to the weight of the engine requires careful design of its components.

This model of a reciprocating engine contains a combination of rigid and flexible parts.

» See model.

This tutorial application demonstrates the modeling of a hinge joint between two bodies in COMSOL Multiphysics. Various nodes available for joints such as Constraints, Locking, Spring, Damper, Prescribed Motion, and Friction are also demonstrated.

Many real structures can be approximated with the double pendulum model. Hence a double pendulum model is chosen in this tutorial.

» See model.

Gyroscopes are used for measuring the orientation or maintaining the stability of airplanes, spacecraft, and submarines vehicles in general. They are also used as sensors in inertial guidance systems.

This model demonstrates the modeling of a mechanical gyroscope. It analyzes the response of the spinning disc to an external torque coming on the disc due to the rotation of the frame. It is shown that the disc is able to maintain it’s orientation when it is spinning with a high speed. This fact can be explained with the principle of conservation of angular momentum.

In the second part of the model, the motion of a spinning top is analyzed. The external torque induced precession and nutation motion of the spinning top is computed.

» See model.

This model demonstrates the ability to simulate Multibody Dynamics in COMSOL. It comprises a multilink mechanism that is used in an antique automobile as a gearshift lever. It was created out of curiosity to find out how large forces are on the individual components. The model uses flexible parts, i.e. the Structural Mechanics Module was used along with the Multibody Dynamics Module.

» See model.

Centrifugal governors, a specific type of governor, control the speed of an engine by regulating the amount of admitted fuel. In order to maintain a near-constant speed, regardless of the load or fuel supply conditions, centrifugal governors use the principle of proportional control. While the governor is in operation, it is critical that it quickly reaches a new steady-state configuration. Hence, the spring and damper design is important.

In the Centrifugal Governor Simulator app, you can perform a rigid body analysis of a spring-loaded centrifugal governor in order to find the sleeve motion, sleeve equilibrium position, and the natural frequency of the system. You can do this by performing a transient analysis to compute the sleeve motion and trajectory of the flyballs, a stationary analysis to compute the equilibrium configuration of the governor, or an eigenfrequency analysis to compute the mode shape of the governor and its damping characteristics.

Many of the geometric parameters can be changed, as well as the spring constant and damping coefficient, and the density of the flyballs and their linkages.

» See model.

Many trucks are equipped with cranes for handling loads. Such cranes have a number of hydraulic cylinders that control the motion of the crane. These cylinders and other components that make up the crane are subjected to large forces when handling heavy loads. In order to determine the load-carrying capacity of the crane, these forces must be computed.

In the Truck-Mounted Crane Analyzer app, a rigid-body analysis of a crane is performed in order to find the payload capacity for the specified orientation and extension of the crane.

Inputs include the angle between the booms, the total extension length, the capacity of the inner and outer boom cylinders, and the capacity extension cylinders. Results from the app include the payload capacity and hydraulic cylinder usage.

» See model.

A centrifugal governor is used to control the speed of rotating machinery. One of the most common applications is in controlling the RPM of an engine by regulating the fuel supply.

This model illustrates the functioning of a spring loaded centrifugal governor. The dynamics of the governor are analyzed under the influence of a centrifugal force, spring force, and damping force. The sleeve motion is studied for two different rotation speeds. The forces and moments experienced by different joints are also computed.

» See model.