circular to oscillatory motion

[COLOR=#000000][FONT=verdana]Hi all[/FONT][/COLOR]

[COLOR=#000000][FONT=verdana]I'm from Bioengineering and unfortunately not too expert on the mechanical side. I'm making a device for which I need a mechanism to transform circular motion into oscillatory motion. I found the mechanism in the picture below:[/FONT][/COLOR]

[ATTACH=CONFIG]1079[/ATTACH]


[COLOR=#000000][FONT=verdana]In my device, the oscillating 'stick' would cover an angle of 170 degrees.[/FONT][/COLOR]

[COLOR=#000000][FONT=verdana]My questions are:[/FONT][/COLOR]
[COLOR=#000000][FONT=verdana]Is the oscillatory motion actually sinusoidal? (ie is the velocity/position actually sinusoidal, or are they just approximated to sinusoids due to the small angle shown in the picture?)[/FONT][/COLOR]
[COLOR=#000000][FONT=verdana]If it is/can be sinusoidal, is there a straight forward way to go about to find the specs (size and position of rotating wheel...) of the system? [/FONT][/COLOR]

[COLOR=#000000][FONT=verdana]Suggestions on different mechanisms I could use are very welcome. (I thought of using a cam but the oscillating 'stick' would in my case probably be jumpy due to the high velocity and low weight needed).[/FONT][/COLOR]

[COLOR=#000000][FONT=verdana]Thanks everyone!![/FONT][/COLOR]

Kinny,

The motion will not be pure sinusoidal, the small angles of the connecting rod will skew the output motion away from a pure sine wave. Why don't you graphically lay out the mechanism and plot the output motion vs. crank angle. From that you should be able to determine if the motion will still work for you. I can tell you that if you connect the con rod to the lever [U]and[/U] the crank with scotch yokes, the result [U]will[/U] be sinusoidal. Or, for a more rigorous analysis, write the equation of motion for the output, only a bit more complicated than a graphical analysis, but still simple geometry.

Timelord

For a quick understanding of a "scotch yoke" see: [url]http://en.wikipedia.org/wiki/Scotch_yoke[/url]

Actually, a slight adjustment in Timelord's and jalbert's answers. Since the motion of the rod is connected to a fixed point on the disc's surface the motion is not truly sinusoidal. Depends on two things: (1) the actual geometry of the connections, and (2) how accurate you really want to be. If the connection was truly as shown in the scotch yoke link above the horizontal position of the rod would be determined by the horizontal position of the connection on the disc. Actually it is dependent on both the horizontal and the vertical position of the connection on the disc. The greater the ratio between the length of the connector arm the the radius of motion of the connection point the closer the motion is to truly sinusoidal. Just to be anal about it...

I rarely counter jboggs inputs, but in this case he is apparently using your arrangement or a piston and crank arrangement as a reference for a scotch yoke design. A true scotch yoke as accurately shown in my above Wikipedia reference does in fact have a true sinusoidal stroke.

JAlberts,

I agree, jboggs is wrong, a scotch yoke gives true sinusoidal motion. I also said that true sinusoidal motion of the output will result only if both ends of the con rod are connected with scotch yokes.

jboggs FYI: By carefully reading your post I get the impression you may have misinterpreted the illustration. In the illustration of a scotch yoke in JAlberts link, its not shown, but the horizontal slider/con rod is constrained in one direction i.e. in this case, it can only slide horizontally, so it only reads the horizontal motion of the crank pin, which is by definition sinusoidal. If I wrong about this misinterpretation, I apologize.

Timelord

Apparently we have had a "failure to communicate". My comments about not being truly sinusoidal were aimed at the OP's illustration, not the scotch yoke diagram. I should have been more clear. The OP's diagram is not truly sinusoidal, the scotch yoke diagram is.