Homework7sol.fall10

# Homework7sol.fall10 - ME 560 Kinematics Fall Semester 2010...

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1 ME 560 Kinematics Fall Semester 2010 Homework No. 7 Monday, November 8th This homework set is based on Chapters 7 and 9 of the required text by Uicker, et al., see Sections 7.1 to 7.11, pages 330 – 361, and Sections 9.1 to 9.6, pages 388 – 405. Problem 1. Solve Problem 7.13, see page 362. Problem 2. Solve Problem 7.15, see page 362. Problem 3. Solve Problem 9.2, see page 415. Problem 4. Solve Problem 9.4, see page 415. Problem 5. Solve Problem 9.8, see page 416.

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2 Solution to Homework Set 7. Problem 7.13. A 4-tooth/in diametral pitch, 24-tooth pinion is to drive a 36-tooth gear. The gears are cut on the 20° full-depth involute system. Find and tabulate the addendum, dedendum, clearance, circular pitch, base pitch, tooth thickness, base circle radii, the length of the paths of approach and recess, and the contact ratio. From Table 7.2, see page 336, the addendum is ( ) 1 1 4 teeth/in 0.250 in aP == = Ans. Also, from Table 7.2, see page 336, the dedendum is ( ) 1.25 1.25 4 teeth/in 0.312 5 in dP = Ans. From the definition on pages 333 and 340, the clearance is ( ) ( ) 0.312 5 in 0.250 in 0.062 5 in cda =−= = Ans. From Equation (7.4), see page 334, the circular pitch is ( ) 4 teeth/in 0.785 4 in/tooth pP ππ = Ans. From Equation (7.6), see page 340, the base pitch is () cos 0.785 4 in/tooth cos20 0.738 0 in/tooth b pp φ ° = Ans. The tooth thickness can be approximated as ( ) 2 0.785 4 in/tooth 2 0.392 7 in tp = Ans. From Equation (7.1), see page 330, the radii of the pitch circles are 2 2 24 teeth 3.000 in 2 2 4 teeth/in N R P = and 3 3 36 teeth 4.500 in 22 4 t e e t h / i n N R P = Ans. Therefore, from Equation (7.15), see page 351, the radii of the base circles are ( ) cos 3.000 in cos20 2.819 in rR ° = and ( ) 33 cos 4.500 in cos20 4.229 in ° = Ans.
3 The length of the arcs (or the paths) of approach and recess. The lengths (or distances) can be measured from a scaled drawing, or they can be calculated from Equations (7.10) and (7.11), see pages 347 and 348. From Figure 7.20, page 348, the arc of approach (from the driven gear; i.e., the pinion 3) is 22

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Homework7sol.fall10 - ME 560 Kinematics Fall Semester 2010...

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