Short Answer:

Constrained motion is the type of motion in which the movement of a body or link is restricted or limited by some conditions or connections. In other words, the body cannot move freely in any direction; its motion is confined to a specific path or manner.

In mechanical systems, constraints are applied to control the type of motion between connected links. For example, in a piston-cylinder arrangement, the piston can only move in a straight line inside the cylinder, showing a type of constrained motion known as completely constrained motion.

Detailed Explanation :

Constrained Motion

In mechanical engineering, especially in the study of mechanisms and kinematics, constrained motion refers to the controlled movement of machine parts or links under specific limitations. These limitations or restrictions ensure that each part moves in a particular way relative to others, maintaining proper functioning of the mechanism. Without constraints, machine parts could move freely in any direction, making the mechanism unstable or non-functional.

A constraint is a condition that limits the motion of a body. It can restrict translation, rotation, or both, depending on the requirement of the machine design. These constraints are essential in mechanisms like engines, pumps, and compressors, where precise and predictable movements are necessary.

Types of Constrained Motion

Constrained motion can be classified into three main types based on the degree and nature of restriction imposed:

1. Completely Constrained Motion:
   This type of motion occurs when a body can move in only one definite direction or path. No other motion is possible except the intended one.
   • Example: The motion of a piston inside a cylinder is completely constrained because it can only move back and forth in a straight line. The cylinder walls prevent any sideways movement.
   • Such motion is very common in mechanical systems like reciprocating engines and hydraulic pumps.
2. Incompletely Constrained Motion:
   In this case, the body can move in more than one direction. The applied constraints are not sufficient to limit all possible movements.
   • Example: A circular shaft placed in a round hole can both rotate and slide along its axis. Hence, its motion is incompletely constrained.
   • To make such motion useful, additional constraints or forces are often applied to limit unwanted movement.
3. Successfully Constrained Motion:
   This type of motion is initially incompletely constrained but becomes completely constrained under the action of an external force or load.
   • Example: The valve of an internal combustion engine is guided by a spring. The valve can rotate or slide, but when the spring force acts, it ensures the valve only moves linearly along its guide.
   • The external force or pressure ensures that only the desired motion occurs during operation.

Importance of Constrained Motion in Mechanisms

Constrained motion is a crucial concept in mechanical design. Without constraints, mechanisms would lose control and precision, leading to failure. Below are some reasons why constrained motion is important:

1. Predictable Movement:
   It ensures that the movement of each link or part in the mechanism follows a definite path, improving accuracy and reliability.
2. Efficient Power Transmission:
   Constrained motion ensures that motion and power are transmitted effectively between machine elements without loss or misalignment.
3. Structural Safety:
   By restricting unwanted movement, constraints help prevent mechanical damage, frictional wear, and system instability.
4. Functional Control:
   Constraints determine how a mechanism performs its operation—whether it converts rotary motion to linear, or vice versa.

Examples of Constrained Motion in Machines

1. Slider-Crank Mechanism:
   The piston’s linear motion inside the cylinder is completely constrained by the crank and connecting rod mechanism.
2. Cam and Follower Mechanism:
   The motion of the follower is successfully constrained due to the contact force between the cam surface and the follower.
3. Door Hinges:
   The motion of a door is completely constrained because it can only rotate about the hinge axis.
4. Lathe Machine:
   The carriage on a lathe bed exhibits constrained motion, allowing it to move only along the guide rails in a straight path.

Mathematical Consideration

In kinematics, the number of constraints helps determine the degree of freedom (DOF) of a body. The degree of freedom refers to the number of independent motions a body can perform.

• When constraints reduce all unnecessary motions and leave only the desired one, the motion is completely constrained.
• For example, a free rigid body in space has 6 degrees of freedom (3 translational + 3 rotational). If constraints remove 5 of these, leaving only one possible motion, it becomes a completely constrained motion.

Applications in Mechanical Systems

1. Engines and Compressors: The piston motion is completely constrained to achieve smooth operation and power conversion.
2. Robotic Arms: Constraints define the controlled movement of each joint to ensure precise operation.
3. Automobiles: Suspension systems and steering mechanisms use constraints to maintain balance and directional control.
4. Manufacturing Machines: Machines like lathes and milling machines rely on constrained motion for accurate machining.

Conclusion:

Constrained motion is a fundamental concept in mechanical engineering that ensures controlled and defined movements of machine parts. By applying suitable constraints, engineers can design mechanisms that operate efficiently and accurately. Whether it is in engines, robotic systems, or industrial machinery, constrained motion maintains the proper relationship between moving elements, ensuring mechanical precision and performance.