04-BS-15 · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams, 04-BS-15 Engineering Graphics & Design Process, 2015-May. Closed-book, no calculator; all 9 questions are of equal value and all must be answered (per the paper’s own instruction "Note: all 9 questions must be answered").
Reference texts: Bertoline & Wiebe, Technical Graphics Communication (4th ed.) — orthographic projection, isometric pictorials, auxiliary and section views, first/third-angle projection; Giesecke et al., Technical Drawing / Engineering Graphics (15th ed.) — ASME Y14.5 / CSA B78.1 dimensioning and sectioning conventions.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
The two parts are a bolt (a cylindrical shank with a hex head) and a square boss with a matching through-hole. A free rigid body in space has 6 total degrees of freedom (DOF): 3 translations (X, Y, Z) and 3 rotations (about X, Y, Z). Assembling the bolt into the boss removes DOF one mating relationship at a time until the bolt is fully located relative to the boss (or, for a bolted joint intended to allow later removal, until only the intentionally-free rotation about the bolt axis remains).
Approach. Apply mates in order of decreasing constraint: a concentric (axis-to-axis) mate first removes the most DOF (2 translations + 2 rotations), then a planar (face-to-face) coincident mate removes the remaining translation along the axis, and finally an angular/keyway or torque relationship removes the last rotational DOF if full constraint (not just a running/rotating fit) is required.
| Step | Relationship applied | DOF removed | DOF remaining |
|---|---|---|---|
| 0 | Two separate free bodies | — | 6 |
| 1 | Concentric mate: bolt shank axis to boss bore axis | 4 (2 lateral translation + 2 tilt rotation) | 2 |
| 2 | Coincident (planar) mate: bolt-head underside to boss top face | 1 (translation along the shared axis) | 1 |
| 3 | Torque/friction from tightening (or a keyway for a locating pin) | 1 (rotation about the shared axis) | 0 — fully constrained |
The concentric mate is applied first because it constrains the most DOF at once (both lateral position and both tilt angles), leaving only translation along, and rotation about, the shared axis — the two DOF a cylindrical mate can never remove by itself. The planar mate then fixes the remaining translation, and tightening the bolt (friction, or a positive feature such as a keyway/dowel for a purely locating pin) removes the final spin DOF.
