The figure shows a crank slider mechanism.

The crank, 2 has length L₂=2L and rotates from an initial angel of 0₂2=1/4 and angular velocity 020-2rad/s

with constant angular acceleration a=3rad/s².

The connecting rod, 2, has a length AB-L3-4L. It also has a rigid portion protruding upwards such that

PBA is a constant angle=/2. The distance PB=1,5L.

The slider, 3, is constrained to move horizontally on a line distance L below the centre of the crank

rotation.

Use the generalised co-ordinate q-[x2,y2,02, X3,3,03, X4,Y4,04]™

Store the results for the calculations of the positions of the links in qq, velocities in vv and accelerations in

aa.

Using length L=10mm, write the Octave script file, cranks.m, and any other function files that may be

required to plot

1) The trajectory of the point P on one figure window

2) The horizontal velocity and acceleration of point P on separate grids on one figure

Submit:

1. Your derivation of the constraint equations

2. The y vector (You may extract this by inspection. No need to differentiate the constraint equations.

3. The Jacobian.

Theory of Machines

Tut 3_23

4. All the necessary m-files

5. A pdf of the two figure windows.

2L

21

2

$

A

1

4L

3

4L

B