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Mechanism Geometry

  • Thread starter Kalus
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  • #1
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Not a homework question, but here seems the most revelant place for this kind of maths.

I have a problem similar to a slider crank but not quite.

http://imageshack.us/photo/my-images/851/sw1b.png/

Fixed points are A and B, all others are free to pivot. The beam labeled 20 is rotating around, at this snapshot 40 degrees from vertical. How can I find how many degrees back and forth the beam that is fixed at A turns in response? I'd quite like to find a general solution

I really can't figure out the geometry for this one :blushing:
 

Answers and Replies

  • #2
45
4
Hi. I tought of a solution but I am not 100% sure it is correct or the simplest one. Let's name the other end of the 20-long beam D and the other end of the 40-long beam C. I think we can use pythagorean theorem for non right angles for this one. First, you can make the triangles ACB and CBD. These triangles share BC. You can calculate BC using the pythagorean theorem for non right angles in both triangles. Thus you will find cos(CDB) as a function of cos(CAB). You can do the same with another pair of triangles: ACD and ADB. So you now have two equations each expressing a relation between two of the 4 angles of the quadrilateral ABDC. We also know that the sum of all interior angles of the quadrilateral is 360 degrees or 2π radians. So far We have 3 equations and 4 unknown angles. We can define angle ABD and find BAC, and since AB is fixed we have our answer. We can define the angle between BD and the dashed line and get ABD since the angle between the dashed line and AB is fixed.
 
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