The GATE Grind

GATE 2023 ME – Question 15

Machining and Machine Tool Operations · Work holding, jigs and fixtures · 1 mark · Multiple choice

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?

four configurations of a cuboidal part resting on vertical pins, with horizontal pins on two side faces. P1 has 3 vertical and 3 horizontal pins (2 + 1). P2 has 4 vertical and 3 horizontal pins. P3 has 3 vertical pins and only 2 horizontal pins. P4 has 4 vertical and 4 horizontal pins.
  1. Configuration P1 arrests 6 degrees of freedom, while Configurations P2 and P4 are over-constrained and Configuration P3 is under-constrained.
  2. Configuration P2 arrests 6 degrees of freedom, while Configurations P1 and P3 are over-constrained and Configuration P4 is under-constrained.
  3. Configuration P3 arrests 6 degrees of freedom, while Configurations P2 and P4 are over-constrained and Configuration P1 is under-constrained.
  4. Configuration P4 arrests 6 degrees of freedom, while Configurations P1 and P3 are over-constrained and Configuration P2 is under-constrained.

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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.

Explanation

A rigid body is located exactly by the 3-2-1 rule: 3 pins on the base (three degrees of freedom), 2 pins on one side face (two more) and 1 pin on an adjacent face (the sixth). That makes 6 pins in all. P1 has 3 + 3 = 6 pins arranged this way, so it arrests exactly 6 degrees of freedom. P2 has 4 + 3 = 7 and P4 has 4 + 4 = 8 pins, so they are over-constrained. P3 has 3 + 2 = 5 pins and so it is under-constrained.