1

ME3001 Dynamics of Machinery Monsoon 2013

Problem set 1 3-8-2013

Exercise 1 Static force analysis of machines (not to be submitted)

Use drawing sheet wherever necessary

1. Sketch the FBD of each link in Fig.1. What is the force P for static equilibrium?

2. In Fig.2 pinion 2 is the driver and gear 3 is an idler. The gears have a diametral pitch of 6 and 20o pressure angle.

Sketch the FBD of gear 3 and show all forces acting. Pinion 2 rotates at 900 rev/min and transmits 25 hp to the

gear set. Fig.2

Fig.1 O2A=100 mm, BA=150mm, BO4=125 mm, CO4=200mm, CD=400mm, O2O4=60mm.

3. Sketch the Free-Body-Diagram (FBD) of each link and show all the forces acing. Obtain the torque T12 to

be applied on link 2 for static equilibrium of the linkage shown in Fig.3. Also, obtain the forces in the

bearings. Work out the solution both graphically and analytically.

4. (Ref. Q3) Obtain the equilibrium torque using the principle of virtual work.

5. ( ,, ) How will you solve the problem using method of superposition?

6. ( ,, ) Consider the following cases (i) there is friction in the joint A (ii) friction in joints A and B and (iii) friction

in all the four joints. Work out the static force analysis in each case assuming direction of impending motion.

(Does the impending motion in a joint imply the same for other joints?)

7. Determine the torque M12 required to drive slider 6 of Fig.4 against a load of P=100N, at a crank angle of θ =

30o.

Fig.4 O2A=63 mm, BC=200mm, BO4=400 mm

Fig.3 AO2=100 mm, CA=350 mm, O2O4=350mm, CO4=250 mm, DO4=175 mm, BA=350 mm, BC=200 mm

2

8. In the Q.7 above, assume a coefficients of friction μ=0.2 between link 1 and 6 and 0.1 between links 3 and 4.

Determine the torque M12 for equilibrium in this case.

9. Use the method of virtual work to analyse the problem 7.

10. A 16 tooth pinion (Fig.5) on shaft 2 rotates at 1720 rev/min and transmits 5 hp to the double reduction gear train.

All gears have 20o pressure angle. The distances between centres of bearings and gears for shaft 3 are shown in

Fig. Find the magnitude and direction of radial force that each bearing exerts against the shaft.

Fig.5

11. Obtain the force transmitted between two spur gears with involute teeth if there is friction between the teeth.

How will the torque ratio (output torque to input torque) vary with respect to the gear rotation? Let N1 and N2 be

the number of teeth, μ is the coefficient of friction, ψ is the pressure angle and m be the module of each gear.

12. Illustrate the effect of friction in a slider-crank mechanism if there is friction in all the joints. A known force P is

applied on the slider. Obtain the torque T to be applied on the crank for static equilibrium. Also obtain all the

bearing forces. Assume a suitable direction for the impending motion. Work out the problem graphically by

assuming numerical values. Indicate the steps involved in the obtaining the forces.

.

Assignment 1 Dynamic force analysis of machines Submit on 13-8-13

Give the entire answers in the drawing sheet.

1. Ref. Pr. 12.7, P.496, Uicker, Pennock and Shigley, Theory of machines and mechanisms, 3rd

ed. 2009. Work out

the problem (i) graphically and (ii) analytically.

2. The crank in the slider-crank mechanism shown in Fig.1 has a constant angular velocity of 100 rad/s ccw. The

mass of the connecting rod is 0.2 kg and the moment of inertia about the centre of mass is 300 kg.mm2.

Determine the crank torque T1 required for dynamic equilibrium at the position shown if slider has a mass of 0.3

kg. Neglect external loads and inertia of crank 1. Work out the problem (a) graphically (b) by method of virtual

work. [Ans: T1=4.4 Nm ccw]

Fig.1