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Unformatted text preview: ECE 594D Robot Locomotion Winter 2010 Homework 4 (due 2/24) 4.1 Lagrangian equations of motion: Two-link pendulum. a) For the system shown in Figure 1, write expressions for T * (the kinetic energy), for V (the potential energy) and for the Lagrangian: L = T *- V . (Hint: write expressions for the position of the mass [e.g., for x m and y m ] and differentiate to find its velocity.) Figure 1: Double-link pendulum with point mass and torque ( τ ) at elbow. b) Find the equations of motion (EOMs) for the system. For each degree of freedom ( q 1 = θ 1 , q 2 = θ 2 ), Ξ i = d dt ∂ L ∂ ˙ q i- ∂ L ∂q i . For this underactuated system, Ξ i = 0 and the second actuation is Ξ i = τ . ( τ appears in only the second EOM because we have used the relative angle at the elbow as the second degree of freedom.) Figure 2: Equations of motion for the acrobot, from  (p.381) (Last revised February 16, 2010) 1 Homework 4 ECE 594D Robot Locomotion Winter 2010 c) This system is really just an acrobot. Show that your solution in part a) is identical to the equations of motion of an acrobot (described, for instance, in Spong’s PFL paper ) if we use...
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- Robot Locomotion