`mjData::cfrc_ext` vs. intuition for “external force” at COM: nonzero torque with an offset weld #3199

wly2014 · 2026-03-27T13:43:28Z

wly2014
Mar 27, 2026

Intro

Hi!

I am a researcher, I use MuJoCo for my research on robot control.

My setup

mujoco C++ 3.6

My question

Summary

In a minimal model (world anchor site + floating body + weld), as shown in figure A, after settling we read cfrc_ext for box_mobile (wrench about body COM, world frame, [τ_x,τ_y,τ_z,f_x,f_y,f_z]).

Program output: torque part nonzero (τ_y ≈ 0.981), force part f_z ≈ 9.81 (m = 1 kg).
Classical-mechanics expectation: the “external” wrench at the site is [0,0.981,0 | 0,0,9.81], as show in the figure B, but at the COM should be [0,0,0 | 0,0,9.81] (no torque, only a vertical force balancing gravity).

Uncertainty: whether cfrc_ext should represent only an “equivalent external force through the COM,” or whether it necessarily includes other moments.

Thanks.

Minimal model and/or code that explain my question

Code

Model: (weld site on box_mobile offset from inertial by pos="0.1 0 0", mass 1 kg).

<?xml version="1.0"?>
<!-- Minimal repro: world anchor site + floating box; weld site at mobile COM. -->
<mujoco model="two_boxes_weld_at_com">
  <compiler angle="radian"/>
  <option timestep="0.001" gravity="0 0 -9.81" iterations="200" tolerance="1e-10"/>
  <size njmax="300" nconmax="50"/>

  <worldbody>
    <light directional="true" diffuse="0.6 0.6 0.6" pos="0 0 2" dir="0 0 -1"/>
    <body name="box_a" pos="0 0 0.5">
      <site name="box_a_weld" pos="0 0 0"/>
      <geom type="box" size="0.3 0.3 0.3" rgba="0.8 0.2 0.2 1" mass="3" contype="0" conaffinity="0"/>
    </body>
    <body name="box_mobile">
      <site name="box_mobile_weld" pos="0.1 0 0"/>
      <freejoint name="box_mobile_freejoint"/>
      <geom type="box" size="0.3 0.3 0.3" rgba="0.2 0.8 0.2 1" mass="1" contype="0" conaffinity="0"/>
    </body>
  </worldbody>

  <equality>
    <weld name="join_world" site1="box_a_weld" site2="box_mobile_weld" solref="0.02 1"
          solimp="0.99 0.99 0.0001 0.35 1"/>
  </equality>

</mujoco>

Code:

#include <mujoco/mujoco.h>

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <string>

namespace {

void print_wrench(FILE* f, const char* label, const double w[6]) {
    std::fprintf(f, "%s [tx ty tz | fx fy fz] = [% .6f % .6f % .6f | % .6f % .6f % .6f]\n", label, w[0], w[1], w[2],
                  w[3], w[4], w[5]);
}

bool run_case(const char* xml_path, const char* body_name, int n_step) {
    char err[4096] = {0};
    mjModel* m = mj_loadXML(xml_path, nullptr, err, sizeof(err));
    if (!m) {
        std::fprintf(stderr, "mj_loadXML failed: %s\n%s\n", xml_path, err);
        return false;
    }
    mjData* d = mj_makeData(m);
    mj_resetDataKeyframe(m, d, 0);

    const int bid = mj_name2id(m, mjOBJ_BODY, body_name);
    if (bid < 0) {
        std::fprintf(stderr, "body not found: %s\n", body_name);
        mj_deleteData(d);
        mj_deleteModel(m);
        return false;
    }

    for (int i = 0; i < n_step; ++i) {
        mj_step(m, d);
    }
    mj_forward(m, d);
    mj_rnePostConstraint(m, d);

    const double* ext = d->cfrc_ext + 6 * bid;
    const double* inw = d->cfrc_int + 6 * bid;

    print_wrench(stdout, "cfrc_ext @COM (world)", ext);
    print_wrench(stdout, "cfrc_int @COM (world)", inw);

    mj_deleteData(d);
    mj_deleteModel(m);
    return true;
}

}  // namespace

int main(int argc, char** argv) {
    const char* models_dir = "./models";
    int n_step = 5000;
    if (argc >= 2) {
        models_dir = argv[1];
    }
    if (argc >= 3) {
        n_step = std::atoi(argv[2]);
    }

    // const std::string at_com = std::string(models_dir) + "/two_boxes_weld_at_com.xml";
    const std::string offset = std::string(models_dir) + "/two_boxes_weld_offset.xml";

    // if (!run_case(at_com.c_str(), "box_mobile", n_step, &r_com)) {
    //     return 2;
    // }
    if (!run_case(offset.c_str(), "box_mobile", n_step)) {
        return 2;
    }

}

Observed output

Typical output in steady state (e.g. mj_step × 5000, timestep=1e-3):

cfrc_ext @COM (world) [tx ty tz | fx fy fz] = [ 0.000000  0.981000 -0.000000 |  0.000000  0.000000  9.810000]
cfrc_int @COM (world) [tx ty tz | fx fy fz] = [-0.000000 -0.981000  0.000000 | -0.000000 -0.000000  0.000000]

Thanks.

Confirmations

I searched the latest documentation thoroughly before posting.
I searched previous Issues and Discussions, I am certain this has not been raised before.

wly2014 · 2026-03-29T07:33:28Z

wly2014
Mar 29, 2026
Author

Furthermore, another confusing phenomenon is that even when the absolute positions of the two boxes remain unchanged, changing the position of the weld site alters the internal and external forces on both the mobile body and box A. According to classical mechanics, if the relative positions of the boxes do not change, their forces should also remain unchanged?

For example, another weld way:

    <body name="box_a" pos="0.1 0 0.5">
      <site name="box_a_weld" pos="-0.1 0 0"/>
      <geom type="box" size="0.3 0.3 0.3" rgba="0.8 0.2 0.2 1" mass="3" contype="0" conaffinity="0"/>
    </body>
    <body name="box_mobile">
      <site name="box_mobile_weld" pos="0 0 0"/>
      <freejoint name="box_mobile_freejoint"/>
      <geom type="box" size="0.3 0.3 0.3" rgba="0.2 0.8 0.2 1" mass="1" contype="0" conaffinity="0"/>
    </body>

Output

cfrc_ext @COM b (world) [tx ty tz | fx fy fz] = [ 0.000000  0.000000  0.000000 |  0.000000  0.000000  9.810000]
cfrc_int @COM b (world) [tx ty tz | fx fy fz] = [ 0.000000  0.000000  0.000000 |  0.000000  0.000000 -0.000000]

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mjData::cfrc_ext vs. intuition for “external force” at COM: nonzero torque with an offset weld #3199

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wly2014 Mar 27, 2026

Intro

My setup

My question

Summary

Minimal model and/or code that explain my question

Code

Observed output

Confirmations

Replies: 1 comment

Uh oh!

wly2014 Mar 29, 2026 Author

`mjData::cfrc_ext` vs. intuition for “external force” at COM: nonzero torque with an offset weld #3199

wly2014
Mar 27, 2026

wly2014
Mar 29, 2026
Author