MIT2_007s09_sol_hw02

MIT2_007s09_sol_hw02 - MIT OpenCourseWare...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 2.007 Design and Manufacturing I Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . F friction_rear Weight sin 20 degrees ( ) F normal_rear F normal_front Weight cos 20 degrees ( ) 20 cm F normal_front 10 cm 3 cm sin 20 degrees ( ) ( ) Weight Page 1 of 8 2.007 Design and Manufacturing 1 Homework #2 Servomotors, Mechanisms & CAD SOLUTION Date Issued: Tuesday 24 FEB, 11AM Date Due: Thursday 5 MAR, 11AM 1) (25 total) Youre building a small, electric-powered vehicle to climb up a 20 degree ramp (similar slope as the ramp into the contest starting box). The vehicle will be operated by two servomotors that can continuously rotate the output shafts that attach directly to wheels on the left and right sides of the vehicle. The manufacturers speci fications indicate each servo is capable of a no load speed of 50 rpm and a stall torque of 0.3 N*m (similar to the specs of the HS-311 standard servos in the kit). The total vehicle weight along with its payload is 12 N (a little more than the weight of a liter of water). All the wheels have a radius of 6cm. The front and rear axles are 20cm apart. The center of gravity of the vehicle and payload is halfway between the front and rear wheels and is 3cm above the surface on which the vehicle runs. A) (5 points) Make a free body diagram of the vehicle driving up a 20 degree ramp after having reached its steady-state velocity. Label each force. Write three equations of equilibrium. Weight= 12N F normal_rear F normal_front F friction_rear F friction_front will be zero if we assume rear-wheel-drive and so this front wheel rotates freely on a bearing Its a good idea to sum forces about this point to minimize the number of terms in the equation. Three Equations of Equilibrium (assuming x is chosen along the direction parallel to the table) Sum forces in the x direction Sum forces in the y direction Sum moments about rear contact point Ramp_ang 20 deg Stall_torque 0.3N m Weight 12 N R wheel 6 cm P servo ( ) ( ) speed car ( ) 6 cm P car Weight ( ) speed car ( ) Weight sin Ramp_ang ( ) V ss R wheel ss Page 2 of 8 B) (5 points) Estimate the steady-state velocity of the vehicle. Sketch the torque-speed curve and power-B) (5 points) Estimate the steady-state velocity of the vehicle....
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This note was uploaded on 02/23/2012 for the course MECHANICAL 2.007 taught by Professor Fry during the Spring '11 term at MIT.

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MIT2_007s09_sol_hw02 - MIT OpenCourseWare...

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