Hinge Joint vs Ball Joint

[meghbhalerao]

Intro

Hi!

I am a graduate student at Rice, I use MuJoCo for my research on Human Modeling.

My setup

MuJoCo version - mujoco==3.2.3
Python.
Hostname and computer details using hostnamectl
$ hostnamectl
Static hostname: xyz
Icon name: computer-desktop
Chassis: desktop 🖥️
Machine ID: xyz
Boot ID: xyz
Operating System: Ubuntu 24.04.3 LTS
Kernel: Linux 6.14.0-37-generic
Architecture: x86-64
Hardware Vendor: Dell Inc.
Hardware Model: Precision 3680
Firmware Version: 1.6.0
Firmware Date: xyz
Firmware Age: xyz

My question

I have 2 things.

1. An output of human motion that is generated my a diffusion model. This essentially is a time series of joint rotations expressed as 6 dimensional rotation representation but this can be converted to a rotation representation of choice, such as a 3 x 3 rotation matrix, or some euler angle type rotation. Of course, this rotation will be with respect to some reference axis.
2. I want to "replay" the above generated motion in Mujoco.
   Here is the xml file that I am using as of now.

<mujoco model="scene">

    <!-- <size njmax="8000" nconmax="4000"/> -->

    <compiler angle="degree" inertiafromgeom="true" coordinate="local"/>
    <!--
        angle="degree"     : human.xml uses degrees for joint ranges
        coordinate="global": joint positions are in world space
        inertiafromgeom    : inertia computed from geometry (needed for physics objects)
    -->

    <visual>
        <headlight ambient=".4 .4 .4" diffuse=".8 .8 .8" specular="0.1 0.1 0.1"/>
        <map znear=".01"/>
        <quality shadowsize="2048"/>
    </visual>

    <!-- <option timestep="0.0333" gravity="0 -9.81 0"/> -->
    <!-- <option timestep="0.0333" gravity="0 0 -9.81 "/> -->
    <option timestep="0.0333" gravity="0 0 0"/>

    <!--
        timestep = 1/30 = 30fps
        gravity is Y-up so gravity points in -Y direction
    -->

    <statistic extent="3" center="0 0 1"/>

    <!-- ===== DEFAULT JOINT/GEOM PROPERTIES (from human.xml) ===== -->
    <default>
        <joint damping="0.0" armature="0.01" stiffness="0.0" limited="true"/>
    <geom group="1" conaffinity="7" condim="1" contype="7" margin="0.001
    " rgba="0.8 0.6 .4 1"/>
    </default>

    <!-- ===== ASSETS: meshes + textures + materials ===== -->
    <asset>
        <!-- Floor texture -->
        <texture builtin="checker" height="100" name="texplane"
                 rgb1="0.15 0.15 0.15" rgb2="0.7 0.7 0.7"
                 type="2d" width="100"/>
        <material name="MatPlane" reflectance="0.3" shininess="0.5"
                  specular="0.5" texrepeat="4 4" texture="texplane"/>

        <!-- Skybox -->
        <texture type="skybox" builtin="gradient"
                 rgb1=".4 .5 .6" rgb2="0 0 0"
                 width="100" height="100"/>

        <!-- Human meshes and materials (from human.xml) -->
        <mesh name="Pelvis" file="meshes/Pelvis.stl"/>
    <mesh name="L_Hip" file="meshes/L_Hip.stl"/>
    <mesh name="R_Hip" file="meshes/R_Hip.stl"/>
    <mesh name="Torso" file="meshes/Torso.stl"/>
    <mesh name="L_Knee" file="meshes/L_Knee.stl"/>
    <mesh name="R_Knee" file="meshes/R_Knee.stl"/>
    <mesh name="Spine" file="meshes/Spine.stl"/>
    <mesh name="L_Ankle" file="meshes/L_Ankle.stl"/>
    <mesh name="R_Ankle" file="meshes/R_Ankle.stl"/>
    <mesh name="Chest" file="meshes/Chest.stl"/>
    <mesh name="L_Toe" file="meshes/L_Toe.stl"/>
    <mesh name="R_Toe" file="meshes/R_Toe.stl"/>
    <mesh name="Neck" file="meshes/Neck.stl"/>
    <mesh name="L_Thorax" file="meshes/L_Thorax.stl"/>
    <mesh name="R_Thorax" file="meshes/R_Thorax.stl"/>
    <mesh name="Head" file="meshes/Head.stl"/>
    <mesh name="L_Shoulder" file="meshes/L_Shoulder.stl"/>
    <mesh name="R_Shoulder" file="meshes/R_Shoulder.stl"/>
    <mesh name="L_Elbow" file="meshes/L_Elbow.stl"/>
    <mesh name="R_Elbow" file="meshes/R_Elbow.stl"/>
    <mesh name="L_Wrist" file="meshes/L_Wrist.stl"/>
    <mesh name="R_Wrist" file="meshes/R_Wrist.stl"/>
    <mesh name="L_Hand" file="meshes/L_Hand.stl"/>
    <mesh name="R_Hand" file="meshes/R_Hand.stl"/>
    </asset>

    <worldbody>

        <!-- ===== LIGHTING ===== -->
        <light name="main_light"
               pos="0 2 2" dir="0 -1 -1"
               diffuse="0.8 0.8 0.8" specular="0.2 0.2 0.2"
               directional="true" castshadow="true"/>

        <light name="fill_light"
               pos="0 2 -2" dir="0 -1 1"
               diffuse="0.3 0.3 0.3" specular="0.0 0.0 0.0"
               directional="true" castshadow="false"/>

        <!-- ===== FLOOR ===== -->
        <geom name="floor" type="plane"
              pos="0 0 0" size="5 5 0.1"
              material="MatPlane"
              conaffinity="1" condim="3" contype="1"/>

        <!-- ===== CAMERAS ===== -->
        <camera name="side_cam"  pos="3 0 0"  xyaxes="0 0 -1 0 1 0"/>
        <camera name="front_cam" pos="0 0 3"  xyaxes="1 0 0 0 1 0"/>

        <!-- ===== HUMAN (merged from human.xml) ===== -->
        <body name="object" mocap="true" pos="0 0 0">
            <body name="Pelvis" pos="0.0 0.0 2" quat="0.707 0.707 0.0000 0.0000">
                <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                <site name="Pelvis" pos="0 0 0" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                <geom group="0" name="Pelvis_collsion" type="mesh" mesh="Pelvis" contype="0" conaffinity="1"/>
                <body name="L_Hip" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                    <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                    <site name="L_Hip" pos="0.0677 -0.3147 0.0214" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                    <joint name="L_Hip_z" type="hinge" pos="0.0677 -0.3147 0.0214" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                    <joint name="L_Hip_y" type="hinge" pos="0.0677 -0.3147 0.0214" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                    <joint name="L_Hip_x" type="hinge" pos="0.0677 -0.3147 0.0214" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                    <geom group="0" name="L_Hip_collision" type="mesh" mesh="L_Hip" contype="0" conaffinity="1"/>
                    <body name="L_Knee" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                        <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                        <site name="L_Knee" pos="0.1020 -0.6899 0.0169" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                        <joint name="L_Knee_z" type="hinge" pos="0.1020 -0.6899 0.0169" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                        <joint name="L_Knee_y" type="hinge" pos="0.1020 -0.6899 0.0169" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                        <joint name="L_Knee_x" type="hinge" pos="0.1020 -0.6899 0.0169" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                        <geom group="0" name="L_Knee_collision" type="mesh" mesh="L_Knee" contype="0" conaffinity="1"/>
                        <body name="L_Ankle" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                            <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                            <site name="L_Ankle" pos="0.0884 -1.0879 -0.0268" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                            <joint name="L_Ankle_z" type="hinge" pos="0.0884 -1.0879 -0.0268" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                            <joint name="L_Ankle_y" type="hinge" pos="0.0884 -1.0879 -0.0268" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                            <joint name="L_Ankle_x" type="hinge" pos="0.0884 -1.0879 -0.0268" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                            <geom group="0" name="L_Ankle_collision" type="mesh" mesh="L_Ankle" contype="0" conaffinity="1"/>
                            <body name="L_Toe" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                <site name="L_Toe" pos="0.1148 -1.1437 0.0925" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                <joint name="L_Toe_z" type="hinge" pos="0.1148 -1.1437 0.0925" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                                <joint name="L_Toe_y" type="hinge" pos="0.1148 -1.1437 0.0925" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                                <joint name="L_Toe_x" type="hinge" pos="0.1148 -1.1437 0.0925" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                                <geom group="0" name="L_Toe_collision" type="mesh" mesh="L_Toe" contype="0" conaffinity="1"/>
                            </body>
                        </body>
                    </body>
                </body>
                <body name="R_Hip" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                    <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                    <site name="R_Hip" pos="-0.0695 -0.3139 0.0239" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                    <joint name="R_Hip_z" type="hinge" pos="-0.0695 -0.3139 0.0239" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                    <joint name="R_Hip_y" type="hinge" pos="-0.0695 -0.3139 0.0239" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                    <joint name="R_Hip_x" type="hinge" pos="-0.0695 -0.3139 0.0239" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                    <geom group="0" name="R_Hip_collision" type="mesh" mesh="R_Hip" contype="0" conaffinity="1"/>
                    <body name="R_Knee" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                        <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                        <site name="R_Knee" pos="-0.1078 -0.6964 0.0150" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                        <joint name="R_Knee_z" type="hinge" pos="-0.1078 -0.6964 0.0150" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                        <joint name="R_Knee_y" type="hinge" pos="-0.1078 -0.6964 0.0150" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                        <joint name="R_Knee_x" type="hinge" pos="-0.1078 -0.6964 0.0150" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                        <geom group="0" name="R_Knee_collision" type="mesh" mesh="R_Knee" contype="0" conaffinity="1"/>
                        <body name="R_Ankle" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                            <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                            <site name="R_Ankle" pos="-0.0920 -1.0948 -0.0273" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                            <joint name="R_Ankle_z" type="hinge" pos="-0.0920 -1.0948 -0.0273" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                            <joint name="R_Ankle_y" type="hinge" pos="-0.0920 -1.0948 -0.0273" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                            <joint name="R_Ankle_x" type="hinge" pos="-0.0920 -1.0948 -0.0273" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                            <geom group="0" name="R_Ankle_collision" type="mesh" mesh="R_Ankle" contype="0" conaffinity="1"/>
                            <body name="R_Toe" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                <site name="R_Toe" pos="-0.1174 -1.1430 0.0961" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                <joint name="R_Toe_z" type="hinge" pos="-0.1174 -1.1430 0.0961" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                                <joint name="R_Toe_y" type="hinge" pos="-0.1174 -1.1430 0.0961" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                                <joint name="R_Toe_x" type="hinge" pos="-0.1174 -1.1430 0.0961" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                                <geom group="0" name="R_Toe_collision" type="mesh" mesh="R_Toe" contype="0" conaffinity="1"/>
                            </body>
                        </body>
                    </body>
                </body>
                <body name="Torso" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                    <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                    <site name="Torso" pos="-0.0043 -0.1144 0.0015" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                    <joint name="Torso_z" type="hinge" pos="-0.0043 -0.1144 0.0015" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                    <joint name="Torso_y" type="hinge" pos="-0.0043 -0.1144 0.0015" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                    <joint name="Torso_x" type="hinge" pos="-0.0043 -0.1144 0.0015" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                    <geom group="0" name="Torso_collision" type="mesh" mesh="Torso" contype="0" conaffinity="1"/>
                    <body name="Spine" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                        <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                        <site name="Spine" pos="0.0012 0.0208 0.0026" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                        <joint name="Spine_z" type="hinge" pos="0.0012 0.0208 0.0026" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                        <joint name="Spine_y" type="hinge" pos="0.0012 0.0208 0.0026" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                        <joint name="Spine_x" type="hinge" pos="0.0012 0.0208 0.0026" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                        <geom group="0" name="Spine_collision" type="mesh" mesh="Spine" contype="0" conaffinity="1"/>
                        <body name="Chest" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                            <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                            <site name="Chest" pos="0.0026 0.0737 0.0280" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                            <joint name="Chest_z" type="hinge" pos="0.0026 0.0737 0.0280" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                            <joint name="Chest_y" type="hinge" pos="0.0026 0.0737 0.0280" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                            <joint name="Chest_x" type="hinge" pos="0.0026 0.0737 0.0280" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                            <geom group="0" name="Chest_collision" type="mesh" mesh="Chest" contype="0" conaffinity="1"/>
                            <body name="Neck" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                <site name="Neck" pos="-0.0002 0.2876 -0.0148" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                <joint name="Neck_z" type="hinge" pos="-0.0002 0.2876 -0.0148" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                                <joint name="Neck_y" type="hinge" pos="-0.0002 0.2876 -0.0148" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                                <joint name="Neck_x" type="hinge" pos="-0.0002 0.2876 -0.0148" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                                <geom group="0" name="Neck_collision" type="mesh" mesh="Neck" contype="0" conaffinity="1"/>
                                <body name="Head" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                    <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                    <site name="Head" pos="0.0050 0.3526 0.0365" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                    <joint name="Head_z" type="hinge" pos="0.0050 0.3526 0.0365" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                                    <joint name="Head_y" type="hinge" pos="0.0050 0.3526 0.0365" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                                    <joint name="Head_x" type="hinge" pos="0.0050 0.3526 0.0365" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                                    <geom group="0" name="Head_collision" type="mesh" mesh="Head" contype="0" conaffinity="1"/>
                                </body>
                            </body>
                            <body name="L_Thorax" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                <site name="L_Thorax" pos="0.0815 0.1955 -0.0060" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                <joint name="L_Thorax_z" type="hinge" pos="0.0815 0.1955 -0.0060" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                                <joint name="L_Thorax_y" type="hinge" pos="0.0815 0.1955 -0.0060" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                                <joint name="L_Thorax_x" type="hinge" pos="0.0815 0.1955 -0.0060" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                                <geom group="0" name="L_Thorax_collision" type="mesh" mesh="L_Thorax" contype="0" conaffinity="1"/>
                                <body name="L_Shoulder" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                    <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                    <site name="L_Shoulder" pos="0.1724 0.2260 -0.0149" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                    <joint name="L_Shoulder_z" type="hinge" pos="0.1724 0.2260 -0.0149" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                                    <joint name="L_Shoulder_y" type="hinge" pos="0.1724 0.2260 -0.0149" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                                    <joint name="L_Shoulder_x" type="hinge" pos="0.1724 0.2260 -0.0149" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                                    <geom group="0" name="L_Shoulder_collision" type="mesh" mesh="L_Shoulder" contype="0" conaffinity="1"/>
                                    <body name="L_Elbow" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                        <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                        <site name="L_Elbow" pos="0.4320 0.2132 -0.0424" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                        <joint name="L_Elbow_z" type="hinge" pos="0.4320 0.2132 -0.0424" axis="0.0000 0.0000 1.0000" range="-720.0000 720.0000"/>
                                        <joint name="L_Elbow_y" type="hinge" pos="0.4320 0.2132 -0.0424" axis="0.0000 1.0000 0.0000" range="-720.0000 720.0000"/>
                                        <joint name="L_Elbow_x" type="hinge" pos="0.4320 0.2132 -0.0424" axis="1.0000 0.0000 0.0000" range="-720.0000 720.0000"/>
                                        <geom group="0" name="L_Elbow_collision" type="mesh" mesh="L_Elbow" contype="0" conaffinity="1"/>
                                        <body name="L_Wrist" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                            <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                            <site name="L_Wrist" pos="0.6813 0.2222 -0.0435" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                            <joint name="L_Wrist_z" type="hinge" pos="0.6813 0.2222 -0.0435" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                                            <joint name="L_Wrist_y" type="hinge" pos="0.6813 0.2222 -0.0435" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                                            <joint name="L_Wrist_x" type="hinge" pos="0.6813 0.2222 -0.0435" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                                            <geom group="0" name="L_Wrist_collision" type="mesh" mesh="L_Wrist" contype="0" conaffinity="1"/>
                                            <body name="L_Hand" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                                <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                                <site name="L_Hand" pos="0.7653 0.2140 -0.0585" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                                <joint name="L_Hand_z" type="hinge" pos="0.7653 0.2140 -0.0585" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                                                <joint name="L_Hand_y" type="hinge" pos="0.7653 0.2140 -0.0585" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                                                <joint name="L_Hand_x" type="hinge" pos="0.7653 0.2140 -0.0585" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                                                <geom group="0" name="L_Hand_collision" type="mesh" mesh="L_Hand" contype="0" conaffinity="1"/>
                                            </body>
                                        </body>
                                    </body>
                                </body>
                            </body>
                            <body name="R_Thorax" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                <site name="R_Thorax" pos="-0.0791 0.1926 -0.0106" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                <joint name="R_Thorax_z" type="hinge" pos="-0.0791 0.1926 -0.0106" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                                <joint name="R_Thorax_y" type="hinge" pos="-0.0791 0.1926 -0.0106" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                                <joint name="R_Thorax_x" type="hinge" pos="-0.0791 0.1926 -0.0106" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                                <geom group="0" name="R_Thorax_collision" type="mesh" mesh="R_Thorax" contype="0" conaffinity="1"/>
                                <body name="R_Shoulder" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                    <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                    <site name="R_Shoulder" pos="-0.1752 0.2251 -0.0197" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                    <joint name="R_Shoulder_z" type="hinge" pos="-0.1752 0.2251 -0.0197" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                                    <joint name="R_Shoulder_y" type="hinge" pos="-0.1752 0.2251 -0.0197" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                                    <joint name="R_Shoulder_x" type="hinge" pos="-0.1752 0.2251 -0.0197" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                                    <geom group="0" name="R_Shoulder_collision" type="mesh" mesh="R_Shoulder" contype="0" conaffinity="1"/>
                                    <body name="R_Elbow" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                        <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                        <site name="R_Elbow" pos="-0.4289 0.2118 -0.0411" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                        <joint name="R_Elbow_z" type="hinge" pos="-0.4289 0.2118 -0.0411" axis="0.0000 0.0000 1.0000" range="-720.0000 720.0000"/>
                                        <joint name="R_Elbow_y" type="hinge" pos="-0.4289 0.2118 -0.0411" axis="0.0000 1.0000 0.0000" range="-720.0000 720.0000"/>
                                        <joint name="R_Elbow_x" type="hinge" pos="-0.4289 0.2118 -0.0411" axis="1.0000 0.0000 0.0000" range="-720.0000 720.0000"/>
                                        <geom group="0" name="R_Elbow_collision" type="mesh" mesh="R_Elbow" contype="0" conaffinity="1"/>
                                        <body name="R_Wrist" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                            <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                            <site name="R_Wrist" pos="-0.6842 0.2196 -0.0467" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                            <joint name="R_Wrist_z" type="hinge" pos="-0.6842 0.2196 -0.0467" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                                            <joint name="R_Wrist_y" type="hinge" pos="-0.6842 0.2196 -0.0467" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                                            <joint name="R_Wrist_x" type="hinge" pos="-0.6842 0.2196 -0.0467" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                                            <geom group="0" name="R_Wrist_collision" type="mesh" mesh="R_Wrist" contype="0" conaffinity="1"/>
                                            <body name="R_Hand" pos="0.0 0.0 0.0" quat="1.0000 0.0000 0.0000 0.0000">
                                                <inertial pos="0 0 0" mass="1" diaginertia="1 1 1" />
                                                <site name="R_Hand" pos="-0.7688 0.2134 -0.0570" size="0.1 0.1 0.1" rgba="0 0 0 0" type="sphere" group="1"/>
                                                <joint name="R_Hand_z" type="hinge" pos="-0.7688 0.2134 -0.0570" axis="0.0000 0.0000 1.0000" range="-360.0000 360.0000"/>
                                                <joint name="R_Hand_y" type="hinge" pos="-0.7688 0.2134 -0.0570" axis="0.0000 1.0000 0.0000" range="-360.0000 360.0000"/>
                                                <joint name="R_Hand_x" type="hinge" pos="-0.7688 0.2134 -0.0570" axis="1.0000 0.0000 0.0000" range="-360.0000 360.0000"/>
                                                <geom group="0" name="R_Hand_collision" type="mesh" mesh="R_Hand" contype="0" conaffinity="1"/>
                                            </body>
                                        </body>
                                    </body>
                                </body>
                            </body>
                        </body>
                    </body>
                </body>
            </body>
        </body>
        <site rgba="0 0 0 0" size="0.005" pos="0.0 0.0 0.0" name="bottom_site"/>
        <site rgba="0 0 0 0" size="0.005" pos="0.0 0.0 1.8" name="top_site"/>
        <site rgba="0 0 0 0" size="0.005" pos="0.5 0.5 0.0" name="horizontal_radius_site"/>

    </worldbody>

</mujoco>

So, the question that I have is, since I want to "map" the output of my algorithm (i.e. the algorithm that outputs a time series of joint rotations and root position), are 3 hinge joints right to use? Or should I use one single ball joint instead of 3 hinge joints? So, I think my core question is are 3 hinge along 3 linearly independent axes equivalent to a single ball joint?

I am not sure if the mujoco forum is the right place to ask this since this is more of a geometry question, but since I am using mujoco I thought that I can ask this here.

Thanks and I look forward to hearing from you.

Confirmations

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

[Balint-H]

Either can work. Series hinges can have singularity issues which can degrade precision/stability, and will introduce anisotropy in the impedance and joint ranges. This can be a positive or a negative depending on what you are going for. Since it sounds like you only care about the kinematics during human motion, series hinges will work fine and may be perhaps more easily interpretable. If you are comfortable with working with quaternions, ball joints may be a simpler solution in terms of implementing it.