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# 20p11 - Problem 20.11 This problem is an excellent example...

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Sheet1 Page 1 % Problem 20.11 % This problem is an excellent example of rolling contact % and 2 points fixed on a rigid body % Set up problem CONSTANTS WBA,WEA,WAF,WBF,WCF,WDF,WEF % These are angular velocity measure numbers CONSTANTS RA,RB,RC,RD,RE % The radii of the gears will be proportional to the % number of teeth in each gear. % The general solution approach is to form 6 linear % equations in 6 unknown angular velocity measure numbers, % which can then be solved for the desired ratio of measure % numbers. % Form equations by applying the rolling contact constraints. % Rolling contact occurs between A and D, B and C, and % D and E. Furthermore, all points on the axis of C and D % have zero velocity in frame F. Thus, if CO and DO are the % points at the center of C and D respectively, then % V_CO_F> = V_DO_F> = 0>. These velocities give us a known % starting point for using 2 points fixed on a rigid body: % V_CHAT_F> = V_CO_F> + CROSS(W_C_F>,P_CO_CHAT) % V_DHAT_F> = V_DO_F> + CROSS(W_D_F>,P_DO_DHAT)

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20p11 - Problem 20.11 This problem is an excellent example...

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