GATE ME 2023 Set 1 — Question 15

MCQ+1 / -0.33MediumWork Holding & 3-2-1 LocationCNC & Work HoldingManufacturing Processes

Manufacturing Processes → CNC & Work Holding → Work Holding & 3-2-1 Location

Last updated 5 September 2026

Question

A cuboidal part has to be accurately positioned first, arresting six degrees of freedom and then clamped in a fixture, to be used for machining. Locating pins in the form of cylinders with hemi-spherical tips are to be placed on the fixture for positioning. Four different configurations of locating pins are proposed as shown. Which one of the options given is correct?

Correct answer (A) Configuration P1 arrests 6 degrees of freedom, while Configurations P2 and P4 are over-constrained and Configuration P3 is under-constrained. Solution The 3-2-1 principle of location is used to arrest all 6 degrees of freedom (3 translations and 3 rotations) of a cuboidal part: 3 pins on the primary datum surface arrest 3 DOF (1 translation along the normal axis, 2 rotations about the axes in the plane). 2 pins on the secondary datum surface arrest 2 DOF (1 translation, 1 rotation). 1 pin on the tertiary datum surface arrests the final 1 DOF (1 translation). Evaluating the configurations: Configuration P1 : Uses exactly 3 pins on the bottom, 2 on the side, and 1 on the back. This follows the 3-2-1 principle and arrests exactly 6 DOF. Configuration P2 : Uses 3 pins on the bottom, 3 on the side, and 1 on the back (7 pins total). It is over-constrained. Configuration P3 : Uses 2 pins on each of the three faces (6 pins total). While it has 6 pins, it does not provide a stable 3-point contact for a primary plane, making it under-constrained/unstable for precise location. Configuration P4 : Uses 3 pins on each of the three faces (9 pins total). It is highly over-constrained. Thus, Option (A) is the correct statement. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (A) Configuration P1 arrests 6 degrees of freedom, while Configurations P2 and P4 are over-constrained and Configuration P3 is under-constrained. Solution The 3-2-1 principle of location is used to arrest all 6 degrees of freedom (3 translations and 3 rotations) of a cuboidal part: 3 pins on the primary datum surface arrest 3 DOF (1 translation along the normal axis, 2 rotations about the axes in the plane). 2 pins on the secondary datum surface arrest 2 DOF (1 translation, 1 rotation). 1 pin on the tertiary datum surface arrests the final 1 DOF (1 translation). Evaluating the configurations: Configuration P1 : Uses exactly 3 pins on the bottom, 2 on the side, and 1 on the back. This follows the 3-2-1 principle and arrests exactly 6 DOF. Configuration P2 : Uses 3 pins on the bottom, 3 on the side, and 1 on the back (7 pins total). It is over-constrained. Configuration P3 : Uses 2 pins on each of the three faces (6 pins total). While it has 6 pins, it does not provide a stable 3-point contact for a primary plane, making it under-constrained/unstable for precise location. Configuration P4 : Uses 3 pins on each of the three faces (9 pins total). It is highly over-constrained. Thus, Option (A) is the correct statement.

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