KINETICS OF MECHANISM

1. Introduction to Kinetics of Mechanisms

Kinetics of mechanisms deals with the forces and torques acting on machine elements in motion. Unlike kinematics (which studies motion without forces), kinetics considers:

• Inertia forces
• External forces
• Frictional forces
• Dynamic equilibrium

Objective:
To determine forces required to produce motion and stresses developed in machine parts.

2. Difference Between Kinematics and Kinetics

Aspect	Kinematics	Kinetics
Study	Motion only	Motion + Forces
Parameters	Displacement, velocity, acceleration	Force, torque, energy
Application	Motion analysis	Design and strength

3. Types of Forces in Mechanisms

3.1 External Forces

• Applied loads
• Gravity forces
• Spring forces

3.2 Internal Forces

• Forces between links
• Joint reactions

3.3 Inertia Forces

• Due to acceleration of mass
• Opposes motion (Newton’s Second Law)

$$F = m \cdot a$$

4. D’Alembert’s Principle

This is the foundation of kinetics analysis.

It converts a dynamic system into a static system by introducing inertia force.$$\text{Inertia Force} = -m \cdot a$$

So,$$\sum F + (-m a) = 0$$

This helps solve problems using static equilibrium equations.

5. Analysis of Mechanisms

(A) Static Force Analysis

• No acceleration considered
• Used in slow-speed machines

(B) Dynamic Force Analysis

• Acceleration considered
• Used in high-speed machines

6. Inertia Force and Torque

Inertia Force:

$$F_i = m \cdot a$$

Inertia Torque:

$$T_i = I \cdot \alpha$$

Where:

• $I$I = Mass moment of inertia
• $\alpha$α = Angular acceleration

7. Free Body Diagram (FBD)

FBD is essential for kinetics analysis.

Steps:

1. Isolate the link
2. Show all forces acting
3. Include inertia forces
4. Apply equilibrium equations

8. Force Analysis of Reciprocating Engine Mechanism

Components:

• Crank
• Connecting rod
• Piston

Forces:

• Gas force on piston
• Inertia force of piston
• Connecting rod reactions

Important formula:$$F_{inertia} = m \cdot r \cdot \omega^2 (\cos\theta + \frac{\cos2\theta}{n})$$

Where:

• $r$r = crank radius
• $\omega$ω = angular velocity
• $n$n = ratio of rod length to crank radius

9. Turning Moment Diagram

• Shows variation of torque over crank angle
• Important for flywheel design

Key Terms:

• Mean torque
• Maximum torque
• Fluctuation of energy

10. Flywheel

Purpose:

• Stores excess energy
• Maintains uniform speed

Energy stored:

$$E = \frac{1}{2} I \omega^2$$

11. Gyroscopic Effects

Occurs when a rotating body changes its axis.

Gyroscopic Couple:

$$C = I \cdot \omega \cdot \omega_p$$

Where:

• $\omega$ω = spin velocity
• $\omega_p$ωp​ = precession velocity

12. Balancing of Forces

Types:

• Static balancing
• Dynamic balancing

Objective:

• Reduce vibration
• Improve machine life

13. Friction in Mechanisms

Types:

• Sliding friction
• Rolling friction

Effects:

• Energy loss
• Wear and tear

14. Work-Energy Principle

$$Work = Change\ in\ Kinetic\ Energy$$Work=Change in Kinetic Energy $$W = \frac{1}{2}mv^2 – \frac{1}{2}mu^2$$

15. Power in Mechanisms

$$Power = Force \times Velocity$$$$P = T \cdot \omega$$

16. Applications of Kinetics of Mechanisms

• IC Engines
• Turbines
• Pumps
• Automobiles
• Robotics

17. Important Exam Topics

• D’Alembert’s principle
• Inertia forces
• Reciprocating engine analysis
• Flywheel problems
• Turning moment diagram

---