WM1AC · Mechanisms and Machines

Block 1 · 15 credits. How things move and why: the kinematics and kinetics of particles, rigid bodies and mechanisms like gear trains and slider-cranks. The maths is taught alongside the mechanics, so each week has a maths topic and an engineering topic that uses it.

Assessment: A1 computer-based test, 30% (week 5, formula sheet provided) · A2 individual lab report on a geared slider-crank, 70% (week 9).

Textbook: Hibbeler, Engineering Mechanics: Dynamics (and Statics), 14th ed.

Week 1: calculus, vectors and straight-line motion

1. Calculus for kinematics: differentiation and integration, the way mechanics uses them
2. Vectors: components, dot product and cross product
3. Matrices and Cramer’s rule (shared with WM1AD)
4. Rectilinear motion: position, velocity and acceleration in a straight line

Week 2: curves, rotation and implicit differentiation

1. Curvilinear and circular motion: motion along a curve, tangential and normal acceleration
2. Rigid body rotation: translation, fixed-axis rotation and general plane motion
3. Implicit differentiation: differentiating geometry with respect to time

Week 3: mechanisms

1. Gear trains and belt drives: what’s shared at a contact
2. Absolute motion analysis: geometry → velocity → acceleration
3. Relative motion analysis: ${\mathbf{v}}_B={\mathbf{v}}_A+\mathbf{\omega }\times {\mathbf{r}}_{B/A}$
4. Slider-crank worked example: one test-style question that uses every Week 1–3 skill

Week 4: forces and kinetics

1. Forces and moments: moments, Varignon’s theorem, couples and resultants
2. Static equilibrium and free body diagrams: supports, FBDs and solving for reactions
3. Friction and Newton’s second law: friction, $\sum F=ma$, connected bodies and $\sum M=I\alpha$
4. Centre of mass: composite shapes and integrating with strips

Revision

• WM1AC practice questions: test-style questions with hidden worked answers
• WM1AC formula sheet
• glossary