Machine Dynamics

Rigid Body - Distances between any two particles on a body remain constant---in real life we are looking for negligible deformation

Lecture 2 (W04/41)

Relative Motion

where _{BA} is read as "B as seen by $A$".

These equations must be treated as vectors.

Lecture 3 (W05/42)

Instantaneous Centre of Rotation

This is a point with zero velocity at any particular moment.

v_A = 0

v_B = v_{BA}

To find the centre of rotation you can draw to perpendicular lines to velocities from two non stationary points. The centre of rotation will be where the lines intersect.

Point Velocity Projections on Joining Axis

Take two points A and B and their velocities at one instant

\begin{align} v_B &= v_A = v_{BA} \ \text{then } \pmb{v_B} || AB &= \pmb{v_A} || AB + \pmb{v_{BA} || AB \ \text{but } \pmb{v_BA} || AB &\equiv 0 \text{(since \pmb{v_BA} \perp AB)} \ \text{or } \pmb{v_B| || AB &= \pmb{v_A} || AB \ v_B\cos\beta = v_A\cos\alpha \ \end{align}

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