ME-403 Theory of Machines - Jun 2026 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aFigure 1 shows a slider crank mechanism. The crank and connecting rod are $150\,mm$ and $600\,mm$ long respectively and crank rotates at uniform speed of $100\,rpm$ (CW). Determine (a) Angular velocity and angular acceleration of the connecting rod

   

   How to answer

   • State crank length 150 mm, connecting rod 600 mm, speed 100 rpm CW and crank angle 30 deg from Figure 1
   • Write velocity and acceleration loop equations / Klein's construction formulas
   • Calculate angular velocity of connecting rod
   • Calculate angular acceleration of connecting rod
2. 7 Marks
   b(b) Velocity and acceleration of piston.

   

   How to answer

   • Use crank kinematics and connecting rod angular motion from part (a)
   • Calculate velocity of piston / slider C along line of stroke
   • Calculate acceleration of piston using acceleration polygon / analytical formula
   • State magnitude and direction
3. 7 Marks
   aExplain the inversion of a single slider-crank mechanism. Describe any three inversions with neat sketches and their engineering applications.
   How to answer

   • Define inversion of kinematic chain by fixing different links
   • Describe three inversions of single slider-crank with neat sketches
   • Give constructional features of each inversion
   • Give engineering applications e.g. reciprocating engine, Whitworth, slotted lever, hand pump
4. 7 Marks
   bA slider-crank mechanism has a crank radius of $100\,mm$ and a connecting rod length of $450\,mm$. Determine the ratio of connecting rod length to crank radius.
   How to answer

   • Note crank radius 100 mm and connecting rod 450 mm
   • Compute ratio n = l/r
   • State numerical value 4.5
   • Mention significance as obliquity ratio
5. 7 Marks
   aDefine (i) base circle (ii) prime circle (iii) pressure angle with respect to cam profile. Why is it preferable to have a smaller pressure angle in cam design?
   How to answer

   • Define base circle as smallest circle from cam centre to cam profile
   • Define prime circle as smallest circle from cam centre to pitch curve
   • Define pressure angle between normal to pitch curve and follower motion direction
   • Explain why smaller pressure angle reduces side thrust and improves force transmission
6. 7 Marks
   bA radial cam is to give simple harmonic motion (SHM) to a knife edge follower with a lift of $50mm$. The rise takes place with SHM for $120^{\circ}$ of cam rotation. Then there is a dwell for $60^{\circ}$ and the return motion is also SHM for $90^{\circ}$ of cam rotation. The remaining $90^{\circ}$ of cam rotation is dwell. The minimum radius of cam is $50mm$. Calculate the maximum velocity and acceleration during the rise and return motion if the cam rotates at $200\,rpm$.
   How to answer

   • List SHM data: lift 50 mm, rise 120 deg, dwell 60 deg, return 90 deg, dwell 90 deg, min radius 50 mm, N=200 rpm
   • Use SHM formulas $v_{max}=\pi h \omega/(2\beta)$, $a_{max}=\pi^2 h \omega^2/(2\beta^2)$
   • Calculate max velocity and acceleration for rise
   • Calculate max velocity and acceleration for return
7. 7 Marks
   a$30\,KW$ of power is to be transmitted at $450\,rpm$ to a shaft with a speed ratio of $3.5$ through a $20^{\circ}$ stub spur gear drive. The load is steady and continuous. The centre distance is $400mm$ approximately. The pinion material is forged steel hardened to BHN 350 and the gear is made of cast steel hardened to BHN 250. (a) Design a gear drive for strength.
   How to answer

   • List power 30 kW, pinion 450 rpm, ratio 3.5, 20 deg stub, centre distance ~400 mm, BHN 350/250
   • Determine module, teeth, face width from Lewis strength / beam strength
   • Check proportions for steady continuous load
   • Finalize gear drive dimensions for strength
8. 7 Marks
   b(b) Check the design for dynamic load and wear.
   How to answer

   • Use Buckingham dynamic load formula
   • Calculate wear load / Hertzian contact stress
   • Compare allowable vs actual loads
   • Conclude safety for dynamic and wear
9. 7 Marks
   aExplain the construction and working principle of a single-plate clutch. https://www.rgpvonline.com
   How to answer

   • Draw labelled construction: flywheel, pressure plate, friction plate, springs, release mechanism
   • Explain engagement by spring axial force and disengagement by clutch pedal
   • Explain torque transmission by friction on single plate (two surfaces)
10. 7 Marks
    bA single-plate clutch has an outer radius of $150\,mm$ and an inner radius of $75\,mm$. The axial force is $5\,kN$, and the coefficient of friction is $0.3$. Assuming uniform wear, determine the torque transmitted.
    How to answer

    • Note R=150 mm, r=75 mm, W=5 kN, mu=0.3, uniform wear
    • Use mean radius $R_m=(R+r)/2$ and $T=n\mu W R_m$
    • Calculate torque transmitted
    • State result in N-m
11. 7 Marks
    aThe layout of a crossed flat leather belt drive is shown in Figure 2. The belt,$6mm$ thick, transmits $7.5kW$ and operates at a velocity of $13m/s$. The coefficient of friction between the belt and pulley surface is $0.3$ and the permissible tensile stress for the belt material is $1.75N/mm2$. The density of leather is $0.95g/cm^{3}$. Neglecting the sag and slip of the belt, calculate (a) The length and width of the belt.

    

    How to answer

    • Extract crossed belt geometry: D1=250 mm, D2=500 mm, C=1500 mm, thickness 6 mm
    • Use crossed belt length $L=\pi(R+r)+2C+(R+r)^2/C$
    • Apply power-tension relation with centrifugal tension and $\sigma_{allow}$
    • Solve for width from $T_{max}=\sigma b t$
12. 7 Marks
    b(b) Belt tensions on the tight and loose sides.

    

    How to answer

    • Use capstan ratio $T_1/T_2 = e^{\mu\theta}$ with crossed-belt contact angle
    • Include centrifugal tension effect
    • Solve tight-side and loose-side tensions
    • Report $T_1$, $T_2$ values
13. 7 Marks
    aState and explain the law of gearing. Discuss the importance of conjugate tooth profiles in ensuring constant velocity ratio.
    How to answer

    • State law of gearing: common normal passes through pitch point
    • Derive constant angular velocity ratio condition
    • Explain conjugate profiles e.g. involute
    • Discuss importance for smooth uniform motion
14. 7 Marks
    bExplain the concepts of static balancing and dynamic balancing. Discuss the balancing of rotating masses in the same plane and in different planes.
    How to answer

    • Define static balancing: resultant force zero
    • Define dynamic balancing: resultant force and couple zero
    • Explain balancing of masses in same plane
    • Explain balancing in different planes with force and couple polygons
15. 7 Marks
    aDefine a single degree of freedom (SDOF) system. Derive the equation of motion for an undamped free vibration system.
    How to answer

    • Define SDOF as system needing one coordinate
    • Draw undamped spring-mass model with free-body diagram
    • Apply Newton's second law $m\ddot{x}+kx=0$
    • Obtain natural frequency form and solution
16. 7 Marks
    bA spring of stiffness $10\,kN/m$ supports a mass of $25\,kg$. If the mass is displaced by $40\,mm$ and released from rest, determine the natural frequency, maximum velocity, and maximum acceleration.
    How to answer

    • Note k=10 kN/m, m=25 kg, amplitude 40 mm released from rest
    • Compute $\omega_n=\sqrt{k/m}$ and $f_n=\omega_n/2\pi$
    • Compute $v_{max}=A\omega_n$
    • Compute $a_{max}=A\omega_n^2$