Understanding constrained motion is crucial in mechanics. Completely constrained motion refers to a system where all possible degrees of freedom (typically 6 in 3D: 3 translational and 3 rotational) are restricted, preventing any motion.

Motion Constraint Analysis

Let's analyze the degrees of freedom for each scenario:

• Shaft with collars in a circular hole: A shaft in a circular hole primarily allows rotation around its axis. Collars restrict axial movement (translation along the axis). However, rotation is still possible. This is not completely constrained.
• Shaft in a footstep bearing: This setup supports axial load and constrains radial movement, but the shaft can still rotate freely around its axis. This is not completely constrained.
• Square bar in square hole: When a square bar fits snugly within a square hole, it significantly restricts motion. It prevents translation in two perpendicular directions (e.g., y and z) and rotation about the main axis (e.g., x-axis). If the fit is precise and the length constrains axial movement, all 6 degrees of freedom can be restricted. This configuration is considered an example of completely constrained motion.
• Both Option 1 and Option 2: Since options 1 and 2 are not completely constrained, this combined option is incorrect.

Conclusion on Constrained Motion

Based on the analysis, the setup that best represents completely constrained motion among the given choices is a square bar within a square hole, as it offers the potential to restrict all degrees of freedom.