Fig. 2. (A) The direction of the center of mass velocity, v_cm, is perpendicular to the stance limb during the single support inverted pendulum phase of the simplest two-dimensional passive dynamic walker. (B) Each transition to a new stance limb requires redirection of the center of mass velocity, from v_cm^(-) to v_cm⁽⁺⁾ (with the superscripts `-' and `+' denoting the instances immediately before and after impact, respectively), accomplished by an impulsive heel strike, S, acting along the leading limb. S also causes an instantaneous reduction in the magnitude of the center of mass velocity through negative work by the leading limb with (shaded square). To walk at steady speed, an equal amount of positive work is required (see Kuo, 2002; Donelan et al., 2002). The magnitude of W_trans^(-)·, and thus the step-to-step transition cost, depends on v_cm^(-) and the angle between the legs, 2 (Equation 1). (C) When step frequency is kept fixed, v_cm^(-) and 2 are proportional to step length, l, so that W_trans^(-) increases with l⁴ (denoted by the differences in area of the shaded squares.

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