flipper body is formed by a head link and n tail links, with the parameter values given by n=5

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

The equations of motion for the flipper locomotor (See Section 4.1.6 of the posted book, Chapter 4) is given by JO + DÕ + thAO = Bu. (1) rniï+d(0»Ã+ÕAO =0. 

The flipper body is formed by a head link and n tail links, with the parameter values given by n=5, rn.0.OOlkg. t0.lni.

Find the optimal gait to achieve the average velocity r0 = —0.15 mIs (negative r means that the body is moving to left) with the minimum average input power. scribe the process and the result with the numerical values of the optimal frequency [I-IzJ and minimum average power 1mW], and plot the following:

The value of the objective function versus the oscillation frequency 1Hz]. Indicate the optimum by * on the curve. Use “loglog.” 

. Input torque u(t) (mN.mml as a function oft.

. Gait «t) := BTO(t) [deg] as a function of t.

. Phase angles [deg] of , and u, as functions of 1.

. Amplitudes of , (deg] and û, [mNmml as functions of .

. Snapshots of the body during locomotion taken at time instants t = iT/lO for i = 1.. .. , 10.

(In the book chapter, w is the the s-coordinate of the center of gravity of the whole body Here.

however, assume for simplicity that w is the s-coordinate of the right end of the head link, and is given by w(t) = r0t.)

Normalize the phase angles of the phasors û and so that iii is positive real, and use u(t) = [úe’9

as the phasor definition. The time courses should be plotted over the time interval O  t  1 s.

Upload one zipped file containing matlab files, one of which should be the main file that calculates the optimal gait and generates all the plots.

Note: Your answer should look like the figures on the next page.

Attachments:

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