Kinematics of Biped Legs for Humanoid Robots

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This Demonstration describes a kinematic model of biped legs as part of a humanoid robot. Each leg has six degrees of freedom (DOFs): yaw, roll, and pitch at the hip joint, pitch at the knee joint, and pitch and roll at the ankle joint.


Forward kinematics use Denavit–Hartenberg (D–H) notation to propagate link transformations from the base to the end effector. The reference coordinate is defined with origin at the intersection point of joints. Inverse kinematics are applied to simplify the calculations. The ankle joint is positioned so that the bottom of the foot rests on the floor surface. The leg's orientation is specified by the angle of rotation of the reference coordinate in the X-Y plane, so that foot's position can be described by a single variable.


Contributed by: Frederick Wu (February 2015)
Open content licensed under CC BY-NC-SA




[1] J. Denavit and R. S. Hartenberg, "A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices," Journal of Applied Mechanics, 22(2), 1955 pp. 215–221.

[2] B. Siciliano and O. Khatib, Springer Handbook of Robotics, Berlin: Springer–Verlag, 2008.

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