What is a planar mechanism?

Short Answer:

A planar mechanism is a type of mechanism in which all the links move in parallel planes or in the same geometric plane. In other words, the motion of every link in a planar mechanism is confined to two dimensions — usually within the X and Y axes.

Such mechanisms are very common in machines and mechanical systems because they are easy to design, analyze, and manufacture. Examples include the four-bar linkage, slider-crank mechanism, and scissor lift mechanism, where all the components move in a single plane.

Detailed Explanation :

Planar Mechanism

A planar mechanism is one of the most widely used mechanisms in mechanical engineering. It refers to a system of interconnected rigid bodies, called links, that move relative to each other in such a way that their motion is restricted to a single plane or parallel planes.

In simple words, if all parts of a mechanism move in a two-dimensional plane — without any motion out of that plane — the mechanism is known as a planar mechanism. The motion of such mechanisms can be easily represented on paper using geometric drawings because they involve only two translational directions and one rotational movement (in-plane).

Planar mechanisms form the basis of most engineering machines such as engines, robotic arms, presses, and tools used in industries.

Definition

A planar mechanism can be defined as:

“A mechanism in which all the moving links have motion confined to one plane or to parallel planes is called a planar mechanism.”

In this type of mechanism, every point on each link moves in a plane that is parallel to the reference plane (the ground plane). Thus, the analysis of motion involves only two dimensions (x and y) and rotation about a perpendicular axis (z-axis).

Characteristics of Planar Mechanism

  1. Two-Dimensional Motion:
    All the movements take place in one plane. There are no out-of-plane or 3D motions.
  2. Parallel Axes:
    The axes of all revolute (rotational) pairs are parallel to one another and perpendicular to the plane of motion.
  3. Degrees of Freedom:
    A rigid body in a plane has three degrees of freedom — two translational (along x and y) and one rotational (about z).
  4. Simplified Analysis:
    Since the motion occurs in one plane, equations of motion and force analysis are simpler compared to spatial mechanisms.
  5. Common in Machines:
    Most practical mechanisms such as engines, linkages, and presses use planar motion due to ease of design and control.

Explanation of Planar Mechanism

In a planar mechanism, multiple rigid links are connected through lower pairs (like turning or sliding joints) that allow relative motion between them. Because all joints lie in the same plane, the relative motion between links is limited to rotation or sliding within that plane.

Each link can have the following possible motions in a planar mechanism:

  • Translational motion: Linear movement of a link (e.g., piston in a cylinder).
  • Rotational motion: Turning motion of a link about a fixed point or axis (e.g., crank in an engine).
  • Combined motion: Both rotation and translation occurring together (e.g., connecting rod in a slider-crank mechanism).

This combination of motions allows planar mechanisms to perform complex functions such as converting rotary motion to linear motion or vice versa.

Degrees of Freedom in Planar Mechanism

The degrees of freedom (DOF) of a planar mechanism represent the number of independent movements possible within the plane. It can be calculated using Grübler’s equation (also known as Kutzbach’s criterion):

Where,
= Degrees of freedom of the mechanism
= Number of links (including the frame)
= Number of lower pairs (like revolute or sliding joints)
= Number of higher pairs (like cam or gear contacts)

For most planar mechanisms, the DOF equals 1, meaning that the motion of one link (input link) determines the motion of all other links.

Examples of Planar Mechanisms

  1. Four-Bar Chain Mechanism:
    • Consists of four rigid links connected by four revolute joints.
    • One link is fixed (the frame), while the others move in the same plane.
    • Used in linkages, levers, and folding arms.
  2. Slider-Crank Mechanism:
    • Converts rotary motion into reciprocating motion or vice versa.
    • Found in internal combustion engines, compressors, and pumps.
    • All parts (crank, connecting rod, and piston) move in a single plane.
  3. Double Slider-Crank Mechanism:
    • Contains two sliding pairs and two turning pairs.
    • Used in mechanisms like Oldham’s coupling and elliptical trammel.
  4. Scissor Lift Mechanism:
    • Consists of several pairs of links connected by pivots, all moving in one plane.
    • Used for lifting loads vertically while keeping the links confined to a single plane.
  5. Beam Engine Mechanism:
    • Used in early steam engines.
    • Converts reciprocating motion of the piston into rotary motion of a flywheel.

Applications of Planar Mechanism

  1. Automotive Engineering:
    Used in engines, steering systems, and suspension linkages.
  2. Manufacturing Machines:
    Applied in shaping machines, slotting machines, and presses for controlled motion.
  3. Robotics:
    Used in planar robotic arms for precise two-dimensional movement.
  4. Aerospace and Defense:
    Mechanisms in landing gears, missile fins, and deployable wings work on planar motion.
  5. Household Devices:
    Common in scissors, window wipers, and door hinges.

Advantages of Planar Mechanisms

  1. Simple Construction and Analysis:
    Since motion occurs in a single plane, the design and mathematical modeling are easy.
  2. Efficient Power Transmission:
    Forces and motion can be transmitted smoothly with minimal losses.
  3. Compact Design:
    Requires less space compared to spatial mechanisms.
  4. High Reliability:
    Fewer components and controlled movements ensure durability and low maintenance.
  5. Versatility:
    Can perform a wide range of functions — from lifting to rotating and reciprocating motion.

Importance in Mechanical Engineering

Planar mechanisms are the building blocks of mechanical systems. They help engineers:

  • Understand motion relationships between connected parts.
  • Design machines that perform specific tasks efficiently.
  • Simplify dynamic and kinematic analysis due to restricted motion.
  • Serve as prototypes for developing three-dimensional mechanisms.

Thus, mastering planar mechanisms is essential for machine design, automation, and robotics.

Conclusion

A planar mechanism is a mechanical system where all parts move in a single plane or in parallel planes. Its motion is two-dimensional, involving translation and rotation within the plane. These mechanisms form the foundation of most engineering machines due to their simplicity, efficiency, and ease of analysis. Examples like the four-bar chain and slider-crank mechanisms are widely used in engines, tools, and robotics. Hence, planar mechanisms are crucial for achieving reliable and controlled motion in modern mechanical engineering systems.