notes/uni/mmme/2046_dynamics_and_control/dynamics.md

---
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)