Discussion
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?
Answer: A
The correct statement is that Configuration P1 arrests 6 degrees of freedom, while P2 and P4 are over-constrained and P3 is under-constrained.
A cuboid is located by the 3-2-1 principle: three pins under the largest face fix one translation and two rotations, two pins on a side face fix a further translation and rotation, and one pin on the adjacent end face fixes the last translation, six points for six degrees of freedom.
- P1: three pins below and three on the sides, in the 3-2-1 pattern, so exactly 6.
- P2: four pins below and three on the sides, 7 in all; one is redundant, so it is over-constrained.
- P3: three below and only two on the sides, 5 in all; one freedom is left, so it is under-constrained.
- P4: four below and four on the sides, 8 in all; over-constrained.
Each of the other options puts the correct 3-2-1 label on a configuration with too many or too few pins.
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