57 lines
1.4 KiB
Markdown
Executable File
57 lines
1.4 KiB
Markdown
Executable File
---
|
|
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
|
|
|
|
|
|
|
|
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}
|
|
|
|
# zack.jpg
|
|
|
|
|