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I have been working on attempting to replicate the following robot developed by some MIT graduates.

https://dspace.mit.edu/handle/1721.1/98948

Presently, I am trying to work out the model for a single leg. That would include obviously both links and joints. My hope is to simulate it in ROS2 with Gazebo and some motor controller modules.

I am fairly new to robotics and all the material I have been studying focuses on robots that are structured with a base link, then some set of joints and links that finishes with the end effector. In my case for the leg of this robot, it seems that I have 5 joints, two that connect to the base (effectively the motor rotors) and then three free joints (connections between (1) left femur and left shin, (2) right femur and right shin, and (3) left shin and right shin). The base link would be the body of the robot that holds all four legs together. My understanding would be that the foot would be the end effector and I would use both motors to actuate the position of the foot. Each leg would be a 2DOF system since the foot can only move on a plane and there is no orientation control of the foot for a given position.

I am trying to understand how this sort of model fits into what I am currently learning about forward and inverse kinematics.

What techniques would be used to model and analyze this system? How might one establish Denavit Hartenberg params for joints that will have rotation based on the rotation of other joint (ie free joints.)

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Most tutorials about kinematics and dynamics would teach you open-chain systems, like the typical robotic manipulator. While in this robot, the leg itself is a closed-chain system, which is quite different and indeed much more complicated. You can have a look at Chapter of Modern Robotics if you are really interested.

You're right the leg has 2 DoF and the foot-tip could be regarded as an end-effector when you try to do some analysis. I know little about closed-loop chain system kinematics and dynamics so I'm not able to give you more insights. But I would recommend you not to focus on DH params too much, because I think DH params are just providing a way to establish coordinate frames. Actually, it doesn't matter how you establish these frames and you can always use Generalized Transformation matrices to compute kinematics.

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