Kinematic tree

The mechanical structure of legged robots is a kinematic tree of revolute joints, with the root of the tree at e.g. the torso of the beast, and one branch for each limb. Motors located in each joint produce torques, which in turn generate a chain of forces between the rigid bodies of the kinematic tree until end-effectors, hands or feet. If the end-effector is free (like a hand in the air), it will perform a pure motion. If it is in contact (like a foot on the ground), it will not move directly, but the interaction with the environment will produce contact forces that in turn move the location of the humanoid in space via the Newton-Euler equations of motion. This phenomenon is central to locomotion, and it can be expressed, like all rigid-body motions, within the framework of screw theory.

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