--- author: Akbar Rahman date: \today title: MMME2046 // Dynamics tags: [ mmme2046, uon, uni, dynamics ] uuid: 98a5449a-02d3-492c-9d0e-3d3eb74baab5 --- # 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 ![](./images/vimscrot-2022-10-17T09:09:23,080550083+01:00.png) 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. ![](./images/vimscrot-2022-10-17T09:13:09,972195575+01:00.png) $$v_A = 0$$ $$v_B = v_{BA}$$ 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. ![](./images/vimscrot-2022-10-17T09:14:37,194818034+01:00.png) ## 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} # zack.jpg ![zack.jpg](./images/zack.jpg)