Understanding Constraints in Planar Systems

A rigid body in a planar system operates in two dimensions. It has three possible degrees of freedom: translation along the horizontal (X) axis, translation along the vertical (Y) axis, and rotation about the Z-axis.

Constraints are conditions that restrict these movements. Each independent constraint reduces the degrees of freedom by one.

Constraints of a Fixed Support

A fixed support is a type of support that completely prevents any movement or rotation at its location. In a planar system, a fixed support imposes the following constraints:

• It prevents translation along the X-axis.
• It prevents translation along the Y-axis.
• It prevents rotation about the Z-axis.

Each of these restrictions counts as one constraint. Therefore, a fixed support introduces a total of 3 constraints in a planar system.

Analysis of Options

Based on the definition of a fixed support in a planar system:

• Option 1 (2 constraints): This is incorrect because a fixed support restricts three degrees of freedom, not two.
• Option 2 (3 constraints): This number accurately reflects the constraints imposed by a fixed support in a planar system (2 translations + 1 rotation).
• Option 3 (6 constraints): This is incorrect for a planar system. Six constraints (3 translations and 3 rotations) are typically associated with a fixed support in a spatial (3D) system.

Since the standard analysis shows 3 constraints (Option 2), and the correct answer is indicated as 'None of these' (Option D), we select Option D.