External forces

The external forces are used to impose a solicitation from the environment on to the system:

  • The solicitation consists of applying an external force and/or an external torque on the body;

  • The three components of the force and/or torque must be calculated by the user in the user_ExtForces function;

  • The application point is defined in MBsysPad and its kinematics is provided in the input of the user_ExtForces;

  • The user_ExtForces function must return:

    • the 3 components of the force in the inertial frame;

    • the 3 components of the torque in the inertial frame;

    • the 3 components of the application point in the body fixed frame, which allows to modify the position where the force is applied;

  • Each external force is associated with a “F sensor” which give the kinematics of the application point;

The user_ExtForces function is called by the mbs_extforces_xxx function (automatically generated) which compute the kinematics of the force application point and resulting force and moment on each body with respect to the center of mass.

Flow chart of the function call for computing external forces

Back to the pendulum-spring example

The goal is to add a wall next to the pendulum with the following assumptions:

  • The end of the pendulum hits the wall;

  • The thickness of the pendulum is neglected;

  • The wall is modelled as a spring in the horizontal direction with a stiffness K = 10 kN/m.

An external force is added at the end of the pendulum in order to model the wall contact.

Schematic representation of the new system


Step 2, 4 and 5 are not impacted by theses modifications.

Step 1: Draw your multibody system

  • Open the Pendulum Spring model in MBsysPad;

  • Add an anchor on the pendulum;

    • Enter the coordinates to locate the point at the end of the pendulum;

  • Add the external force:

    • Click on the ExtForce button;

    • Click on the anchor point at the end of the pendulum;

    • A “F” is added next to the anchor point;

    • Click on the “F” to edit its properties and give it a name;

Step 2: Generate your multibody equations

You have to generate the multibody equations after the creation of an external force. You also need to regenerate the user models files.

Step 3: Write your user function

Edit the user_ExtForces function (open the file from the userfctR subfolder of your project) and write the force equations.

  • You have to include user_all_id.h;

  • You have to declare the variable outside the switch-case;

#include "user_all_id.h"
double* user_ExtForces(double PxF[4], double RxF[4][4],
                       double VxF[4], double OMxF[4],
                       double AxF[4], double OMPxF[4],
                       MbsData *mbs_data, double tsim,int ixF)

    /* Begin of user declaration */
    double gap, K;
    /* End of user declaration */


    /* Begin of user code */

        case LateralBumpstop_id:
            gap = 0.3;
            K = 10000;
            if (PxF[1]>gap)
                Fx = -K * (PxF[1] - gap);

    /* End of user code */

    return Swr


By default, the dxF components to the position of the anchor point defined in MBsysPad using the following commands (see the first commands of the user_ExtForces function):

  • idpt = mbs_data->xfidpt[ixF];

  • dxF[1] = mbs_data->dpt[1][idpt];

  • dxF[2] = mbs_data->dpt[2][idpt];

  • dxF[3] = mbs_data->dpt[3][idpt];

This behaviour can be modified if the force application point is moving with respect to the body (example: wheel/ground contact).


If there are several external forces in the model, all the constitutive laws are introduced in the user_ExtForces function and the switch-case is used to distinguish the various forces.

Step 4: Run your simulation


Keeping initial joint angle of 1 [rad] for pendulum leads to an initial position deep in the wall => generating high forces. This might be intractable for the simulation. To avoid this set initial angle at -0.1 [rad].

Check the results

Plot the graph of the joint position (results ares available in resultsR/ folder) and check your results with the following graph.

Plot the time history of the joint position of the pendulum spring example

Time history of the joint position