How to correctly use slider-crank transmission for cylinders? #374

rohit-kumar-j · 2022-07-07T06:49:59Z

rohit-kumar-j
Jul 7, 2022

I have a equality/connect for linking a part my robot,(ref image) the rod of the cylinder is connected to the arm via an equality constaraint like so: (similar to a crank-slider)

XML Structure

<body name="parent_1">
    <geom name="parent_1_geom" type="mesh" mesh="parent_1_mesh" />
    <body name="arm" >
        <joint name="joint_arm" type="hinge" />
        <geom name="arm_geom" type="mesh" mesh="arm_mesh" />
    </body>
    <body name="parent_2" >
        <joint name="connecting_joint" type="hinge" />
        <geom name="parent_2_geom" type="mesh" mesh="parent_2_mesh"/>
        <body name="rod" >
            <joint name="joint_rod" type="slide"/>
            <geom name="rod_geom" type="mesh" mesh="rod_mesh" />
        </body>
    </body>
</body>

<equality>
    <connect name="connect_1" body1="rod" body2="arm" anchor=" some_x some_y some_z" />
</equality>

<actuator>
    <position name="position_actuator_rod" joint="joint_rod" kp="100" />
    <position name="position_actuator_arm" joint="joint_arm" kp="100" />
</actuator>

1.Parent_1, 2.Parent_2, 3. Rod, 4. Arm

I use the following to control the rod to move the arm, the equality seems to disappear:

Equality/connect seems to disappear

id = mujoco.mj_name2id(
        model,
        mujoco.mjtObj.mjOBJ_ACTUATOR,
        "position_actuator_rod") # This joint is slide, inbetween body 2 and 3
data.ctrl[id] = some_changing_value

mujoco_equality_ctrl_problem_1.1.mp4

Equality/connect works the other way

id = mujoco.mj_name2id(
        model,
        mujoco.mjtObj.mjOBJ_ACTUATOR,
        "position_actuator_arm") # This joint is revolute, inbetween body 4 and 1
data.ctrl[id] = some_changing_value

mujoco_equality_ctrl_problem_1.2.mp4

Answered by yuvaltassa

Jul 8, 2022

MuJoCo's mechanism supports both of these.
Did you actually load my example model in simulate and play with it?

Here is a model that shows how to make both forward and backward slider-cranks, and includes an example of a "broken" mechanism which cannot maintain the requested relationship at the initial state.

educational slider-crank model

<mujoco model="slider-crank">
  <!-- these are the visual properties associated with the slider-crank mechanism: -->
  <visual>
    <scale slidercrank=".1"/>
    <rgba slidercrank="0.5 0.4 0.8 1" crankbroken="0.0 0.6 0.2 1"/>
  </visual>

  <!-- defining some defaults for readability -->
  <default>
    <position ctrllimited="true" ctrlrange="-.1 .1" kp="

View full answer

yuvaltassa · 2022-07-07T07:16:03Z

yuvaltassa
Jul 7, 2022
Maintainer

I'll look more carefully soon at the details, but if you are trying to implement a slider-crank you should know that MuJuCo has a native slider-crank transmission type (search the docs, I'm currently AFK), equality constraints not required.

0 replies

yuvaltassa · 2022-07-07T09:55:38Z

yuvaltassa
Jul 7, 2022
Maintainer

Having taken a look, I can't really reproduce what you are seeing so can't really diagnose. If you are still experiencing a strange issue, please attach a full loadable model as a zip file and I'll take a look.

However as I said, if you have slider-cranks in your model you should use the build-in slider-crank transmission mechanism, as it adds no DoFs or equality constraints to your model and is significantly more efficient than your current approach (which is also valid, just less efficient). Here is a minimal model implementing a slider-crank. Note that it has exactly 1 DoF. Load it in simulate and play with it to understand how it works.

<mujoco>
  <worldbody>
    <site name="slidersite" pos="0 -.1 0" zaxis="0 1 0" size=".012" rgba="1 0 0 1"/>
    <body>
      <joint damping=".1"/>
      <geom type="capsule" size=".01" fromto="0 0 0 .2 0 0"/>
      <site name="cranksite" pos=".1 0 0" size=".012" rgba="1 0 0 1"/>
    </body>
  </worldbody>

  <actuator>
    <position name="slider-crank" cranksite="cranksite" slidersite="slidersite" cranklength=".11" 
      ctrllimited="true" ctrlrange="-.1 .1" kp="30"/>
  </actuator>
</mujoco>

slider-crank transmissions are currently not well documented. Let us know if you end up using this and we might add better documentation.

1 reply

rohit-kumar-j Jul 7, 2022
Author

A labeled diagram with the slider-crank assembly with the terms cranklength and slider position would be helpful.

rohit-kumar-j · 2022-07-08T07:08:21Z

rohit-kumar-j
Jul 8, 2022
Author

I apologize for the inaccurate explanation on my part,
I think the slider-crank in mujoco is similar to this:

I wanted to create this:

Do you have an example xml for the same?

0 replies

yuvaltassa · 2022-07-08T10:25:52Z

yuvaltassa
Jul 8, 2022
Maintainer

MuJoCo's mechanism supports both of these.
Did you actually load my example model in simulate and play with it?

Here is a model that shows how to make both forward and backward slider-cranks, and includes an example of a "broken" mechanism which cannot maintain the requested relationship at the initial state.

educational slider-crank model

<mujoco model="slider-crank">
  <!-- these are the visual properties associated with the slider-crank mechanism: -->
  <visual>
    <scale slidercrank=".1"/>
    <rgba slidercrank="0.5 0.4 0.8 1" crankbroken="0.0 0.6 0.2 1"/>
  </visual>

  <!-- defining some defaults for readability -->
  <default>
    <position ctrllimited="true" ctrlrange="-.1 .1" kp="30"/>
    <default class="joint">
      <geom type="cylinder" size=".006" fromto="0 0 0 0 0 .05" rgba=".9 .6 1 1"/>
    </default>
    <default class="slidersite">
      <site type="cylinder" size=".01 .015" rgba="1 0 0 1" />
    </default>
    <default class="cranksite">
      <site size=".012" rgba="0 0 1 1" />
    </default>
  </default>

  <worldbody>
    <light pos="0 0 1"/>
    <geom type="plane" size=".5 .5 .01" pos="0 0 -.05"/>
    <site name="slidersite" class="slidersite" pos="0 -.1 0" zaxis="1 .5 0"/>
    <body>
      <joint damping=".1"/>
      <geom class="joint"/>
      <geom type="capsule" size=".01" fromto="0 0 0 .2 0 0"/>
      <site name="cranksite" class="cranksite" pos=".1 0 0"/>
      <site name="cranksite2" class="cranksite" pos=".2 0 0"/>
      <body pos=".15 0 0">
        <joint damping=".1"/>
        <geom class="joint"/>
        <geom type="capsule" size=".01" fromto="0 -.15 0 0 0 0"/>
        <site name="slidersite2" class="slidersite" pos=".02 -.1 0" euler="-90 30 0"/>
      </body>
    </body>
    <site name="slidersite3" class="slidersite" pos="0 .1 0" zaxis="1 .2 0"/>
    <body pos="0 .2 0">
      <joint  damping=".1"/>
      <geom class="joint"/>
      <geom type="capsule" size=".01" fromto="0 0 0 .15 0 0"/>
      <site name="cranksite3" class="cranksite" pos=".1 0 0" size=".012"/>
    </body>
  </worldbody>

  <actuator>
    <!-- forward slider-crank: the slider site is attached to the parent -->
    <position name="forward" cranksite="cranksite" slidersite="slidersite" cranklength=".08"/>
    <!-- backward slider-crank: the slider site is attached to the child -->
    <position name="backward" cranksite="cranksite2" slidersite="slidersite2" cranklength=".06"/>
    <!--  The "broken-crank" actuator is "broken" in the initial state: the crank length is too
          short to maintain the requested geometric relationship -->
    <position name="broken" cranksite="cranksite3" slidersite="slidersite3" cranklength=".05"/>
  </actuator>
</mujoco>

Here is a riddle to check your understanding. The orientation of slidersite is defined using zaxis, but the orientation of slidersite2 is defined using euler. Do you understand why I had to do that? What happens if you try to use zaxis to orient slidersite2? In order to answer this question you'll need to use simulate's site-frame visualisation.

2 replies

yuvaltassa Jul 8, 2022
Maintainer

Having played with it a bit more I realised the same configuration can be created using the zaxis attribute, euler is not actually required, but the important lesson remains -- you need to think about the precise orientation of the slidersite's frame.

yuvaltassa Jul 8, 2022
Maintainer

Note, I added this model to the repo.

rohit-kumar-j · 2022-07-08T18:45:29Z

rohit-kumar-j
Jul 8, 2022
Author

Thank you for the second example(broken-crank), it cleared much confusion.
I did play around with the slider-crank, but with the very first model I ended up with this:

Confused from trail from 1st example

<mujoco>
    <worldbody>
        <body name="fixed_arm" pos="0 -.1 0">
            <geom type="box" size=".01 .09 .01" rgba="1 0 0 .5" />
            <body name="pink_capsule" pos="0 -.1 0" euler="90 153.5 0">
                <joint axis="0 1 0" />
                <geom type="capsule" size=".02 .03" pos="0 0 .1" rgba="1 0 1 .5" />
                <site name="slidersite" pos="0 0 0" zaxis="0 0 1" size=".012" rgba="1 0 0 1" />
                <body name="rod" pos="0 0 .15">
                    <joint name="slide_joint" type="slide" axis="0 0 1" />
                    <geom type="capsule" size=".015 .025" rgba="1 1 .1 1" />
                </body>
            </body>
            <body pos="0 .1 0">
                <joint name="main_pivot" damping=".1" range="-0.5 1.6" limited="true" />
                <geom type="capsule" size=".01" fromto=".02 0 0 .2 0 0" />
                <site name="cranksite" pos=".1 0 0" size=".012" rgba="1 0 0 1" />
                <body name="connecting_box" pos=".1 0 0">
                    <joint />
                    <geom type="box" size=".01 .01 .01" />
                </body>
            </body>
        </body>
    </worldbody>

    <actuator>
        <position name="slider-crank" cranksite="cranksite" slidersite="slidersite" cranklength=".11" kp="200" />
        <!-- ctrllimited="true" ctrlrange="-1 1" kp="30" -->
        <motor name="force_act" joint="slide_joint" gear="1" ctrllimited="true" ctrlrange="-100 100" />
    </actuator>
    <equality>
        <weld body1="connecting_box" body2="rod" />
    </equality>
    <contact>
        <exclude body1="fixed_arm" body2="pink_capsule" />
    </contact>
</mujoco>

mujoco_slider_crank_cylinder.mp4

But ended up having a Misalignment issue when the links were rotated(prehaps due to soft constraints?):

mujoco_slider_crank_misalignment_problem.mp4

Albeit, I did not fully understand the way the slider-crank is supposed to be used. Which part of the generated geom was the slider, and which part was the crank? Why does one of them switch from red to purple as I adjust the actuator value? Why/how is the force from this silder crank not working? etc

The 2nd example of the slider-crank, i.e the educational slider-crank model and your question related to the euler vs zaxis cleared up some of this confusion.

From frame-orientations/zaxis:

This determines the X and Y axes of the frame implicitly. This is useful for geoms with rotational symmetry around the Z axis, as well as lights - which are oriented along the Z axis of their frame.

This makes it easier to use zaxis instead of euler as the orientation is simpler to adjust. The broken slider-crank example (especially with the orientation of the capsule geom) helped me understand why the cylindrical part of the silder-crank behaves a certain way and how to orient the slider-crank.

Broken Crank	Site Frame	Upon Changing `zaxis` to 1 .5 0 (the solution is feasible and the crank is no longer broken)

Solving for Crank

Feasible Solution(the crank is purple, yellow mark is the point of solution)	Feasible Solution Not Feasible (the crank is green, no solution for the visually generated crank, the capsule body rotates, followed by crank color change ,followed by slider shortening when the simulation is played)

If I understand this correctly, mujoco solves and moves the geom for all possible radii of the cranks(black circles) to intersect to the Zaxis of of the slider(purple cylindrical part of the slider-crank) until the cranklength specified in the xml file is reached, at which point, the crankarm turns purple again. Then mujoco prioritizes to reduce the slider position to zero while keeping the cranklength as specified in the xml.

The 1st few seconds of the video below, it appears as if the joint between the green(unsolved) crank and the capsule geom does not change, only after the geom itself is rotated so as not to violate the specified cranklength and the crank color has turned purple,

The slider moves (length of the cylinder reduces to set point, which is zero)
The angle between the crank and the geom varies as a consequence of the slider going to it set point(zero)

Video:

Broken crank: @ timestep=1e-6

mujoco_slider_crank_broken_priority.mp4

So, Ideally for a robot,

Should we make it such that the slider-crank look something like this at startup? (Assuming, we do not want the sudden jerk to pull the slider crank towards each other)
If the site geom does not have the inertial properties, how can we add mass/collision properties from the real robot while not violating soft constraints as seen in Issue: Equality constraint Bounciness or the misalignment video above?

1 reply

rohit-kumar-j Jul 8, 2022
Author

Renaming from:
"Equality/connect + data.ctrl don't work together" to "How to correctly use slider-crank transmission for cylinders?"

rohit-kumar-j · 2022-07-08T19:31:55Z

rohit-kumar-j
Jul 8, 2022
Author

Can we lock joint at the slidersite?

2 replies

yuvaltassa Jul 8, 2022
Maintainer

Just delete the joint? Or add <joint limited="true" range="min max"/>, if that's what you're trying to achieve?

yuvaltassa Jul 8, 2022
Maintainer

Oh, I see what you're asking. That black circle not at the slidersite, that's the connection point of the slider-crank mechanism.

No. You cannot put a limit on that, you can only put joint ranges on the actual joints.

yuvaltassa · 2022-07-08T22:56:01Z

yuvaltassa
Jul 8, 2022
Maintainer

If it helps, here is the slider-crank visualisation code and here is the code computing the transmission (length + moment arm).

Try to think of it in the opposite direction that the force is going. MuJoCo is trying to compute the function: slider_length(joint_angles). Given some joint angles and a predefined crank length cranklength (the "crank" is the thin purple cylinder that is connected to the cranksite), and given the direction of the slidersite z-axis, MuJoCo tries to compute the length of the slider (the thick purple cylinder that is connected to the slidersite)) – in closed-form.

If closed-form is not possible, the crank is "broken" and is coloured in a different colour (I made it green in my example, the default is red).
If it is possible, this length is the length of the actuator. This length can be controlled by e.g. a <position> actuator.

(The reason the function needs to be closed-form is that we care about its Jacobian (the "moment-arm matrix"), not just its value)

0 replies

rohit-kumar-j · 2022-07-21T16:39:09Z

rohit-kumar-j
Jul 21, 2022
Author

For future readers, playing with the time-step, solref and solimp, a combination of a lower time step and a equality/weld did the trick for me:

Video

mujoco_Is_weld_better_than_connect.mp4

XML

<mujoco model="slider-crank">
    <option timestep="0.0001" gravity="0 0 -9.81" collision="predefined" />

    <worldbody>
        <light pos="0 0 1" />
        <geom type="plane" size="3 3 .01" pos="0 0 -.2" />
        <body name="b_root" pos="0 0 2" euler="0 90 0">
            <geom name="g_root_1" type="box" fromto="0 0 0 1 0 0" size="0.05" rgba="0 1 .1 .5" mass="0.0001" />
            <geom name="g_root_2" type="cylinder" fromto="1 0 -.1 1 0 .1" size="0.08" rgba="0 1 .1 1" mass="0.0001" />
            <body name="b_arm" pos="1 0 0">
                <joint name="hinge_joint_j1" type="hinge" />
                <geom name="g_arm_1" type="cylinder" fromto="0 0 -.1 0 0 .1" size="0.08" rgba="1 0 .1 1" mass="0.0001" />
                <geom name="g_arm_2" type="box" fromto="0 0 0 0 1 0" size="0.05" rgba="1 0 .1 .5" mass="0.0001" />
                <geom name="g_arm_3" pos="0 1 0" type="sphere" size="0.03" rgba="1 0 .1 1" mass="1" />
            </body>
            <body name="b_cyl" pos=".2 0 0" euler="0 0 -45">
                <joint name="j2" type="hinge" />
                <geom name="g_cyl_1" type="cylinder" fromto="0 0 -.1 0 0 .1" size="0.03" rgba="1 0 .1 1" mass="0.0001" />
                <geom name="g_cyl_2" type="cylinder" fromto="0 0 0 0 0.565685424949238 0" size="0.05" rgba="1 0 .1 .5" mass="0.0001" />
                <body name="b_piston" pos="0 0.565685424949238 0">
                    <joint name="slide_joint_j3" type="slide" axis="0 1 0" />
                    <geom name="g_piston_1" type="cylinder" fromto="0 0.565685424949238 -.1 0 0.565685424949238 .1" size="0.03" rgba="1 0 .1 1" mass="0.0001" />
                    <geom name="g_piston_2" type="cylinder" fromto="0 0 0 0 0.565685424949238 0" size="0.02" rgba="1 0 .1 .5" mass="0.0001" />
                    <body name="weld_me" pos="0 0.565685424949238 0" euler="0 0 45">
                        <joint name="weld_j" />
                        <geom name="g_piston_weld_2" type="cylinder" fromto="0 0 -.1 0 0 .1" size="0.03" rgba="1 1 .1 1" mass="0.0001" />
                    </body>
                </body>
            </body>
        </body>
        <body name="b_root_1" pos="1 0 2" euler="0 90 0">
            <geom name="g_root_1_1" type="box" fromto="0 0 0 1 0 0" size="0.05" rgba="0 .1 1 .5" mass="0.0001" />
            <geom name="g_root_2_2" type="cylinder" fromto="1 0 -.1 1 0 .1" size="0.08" rgba="0 1 .1 1" mass="0.0001" />
            <body name="b_arm_1" pos="1 0 0">
                <joint name="hinge_joint_j1_1" type="hinge" />
                <geom name="g_arm_1_1" type="cylinder" fromto="0 0 -.1 0 0 .1" size="0.08" rgba="1 0 .1 1" mass="0.0001" />
                <geom name="g_arm_2_1" type="box" fromto="0 0 0 0 1 0" size="0.05" rgba="1 0 .1 .5" mass="0.0001" />
                <geom name="g_arm_3_1" pos="0 1 0" type="sphere" size="0.03" rgba="1 0 .1 1" mass="1" />
            </body>
            <body name="b_cyl_1" pos=".2 0 0" euler="0 0 -45">
                <joint name="j2_1" type="hinge" />
                <geom name="g_cyl_1_1" type="cylinder" fromto="0 0 -.1 0 0 .1" size="0.03" rgba="1 0 .1 1" mass="0.0001" />
                <geom name="g_cyl_2_1" type="cylinder" fromto="0 0 0 0 0.565685424949238 0" size="0.05" rgba="1 0 .1 .5" mass="0.0001" />
                <body name="b_piston_1" pos="0 0.565685424949238 0">
                    <joint name="slide_joint_j3_1" type="slide" axis="0 1 0" />
                    <geom name="g_piston_1_1" type="cylinder" fromto="0 0.565685424949238 -.1 0 0.565685424949238 .1" size="0.03" rgba="1 0 .1 1" mass="0.0001" />
                    <geom name="g_piston_2_1" type="cylinder" fromto="0 0 0 0 0.565685424949238 0" size="0.02" rgba="1 0 .1 .5" mass="0.0001" />
                    <body name="weld_me_1" pos="0 0.565685424949238 0" euler="0 0 45">
                        <joint name="weld_j_1" />
                        <geom name="g_piston_weld_2_1" type="cylinder" fromto="0 0 -.1 0 0 .1" size="0.03" rgba="1 1 .1 1" mass="0.0001" />
                    </body>
                </body>
            </body>
        </body>
    </worldbody>
    <equality>
        <weld name="weld_1" active="true" body1="b_arm" body2="weld_me" relpose="0 0.8 0 1 0 0 0" solref="0.0002 1" />
        <connect name="connect_1_1" active="true" body1="weld_me_1" body2="b_arm_1" anchor="0 0.565685424949238 0" />

    </equality>
    <actuator>
        <!-- <position name="j1_act" joint="hinge_joint_j1" kp="1000" /> -->
        <!-- <position name="j1_act_1" joint="hinge_joint_j1_1" kp="1000" /> -->
        <position name="j3_act" joint="slide_joint_j3" kp="1000" />
        <position name="j3_act_1" joint="slide_joint_j3_1" kp="10" />
    </actuator>
    <sensor>
        <jointpos name="j1_sensor" joint="hinge_joint_j1" />
        <jointpos name="j1_sensor_1" joint="hinge_joint_j1_1" />
    </sensor>
</mujoco>

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How to correctly use slider-crank transmission for cylinders? #374

rohit-kumar-j Jul 7, 2022

1.Parent_1, 2.Parent_2, 3. Rod, 4. Arm

Replies: 8 comments · 6 replies

yuvaltassa Jul 7, 2022 Maintainer

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Solving for Crank

Video:

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