Calculating Rotation Angle in an Offset Slider-Crank Mechanism

[aleset]

I have a offset slider crank mechanism. Of which I know all the geometrical data, because I measure them .

I do not understand how I can calculate the rotation angle of the connecting rod knowing the stroke.in my formula I have the angle b. I do not understand how to eliminate it from the formula

regardes

 

[tnich]

I have a offset slider crank mechanism. Of which I know all the geometrical data, because I measure them .

I do not understand how I can calculate the rotation angle of the connecting rod knowing the stroke.in my formula I have the angle b. I do not understand how to eliminate it from the formula

regardes

You have two unknowns, $a$ and $b$, but only one equation. If you want to solve for $b$, you need one more equation involving $a$ and $b$.

 

[aleset]

thanks thinch.

is there an alternative formula that relates the angle "a" with the stroke "c" without knowing the angle "b"?

 

[Tom.G]

Wrong. See my posts 6 and 7, below.[/color]

Your Known data:

1. Center of rotation of crank. Call this 'γ'
2. Radius of crank, 'r'
3. Angle of crank, 'α'
4. Length of connecting rod, 'L'
5. Location and orientation of stroke 'C' centerline

I'm doing this in rectangular coordinates because I find it easier to think about.

• With the first three knowns ('γ', 'r', 'α') you find crank location, the intersection of 'r' and 'L'. Call this point 'δ'
• Find the point(s) on a circle centered at 'δ', of radius 'L', that intersect the line that describes the stroke 'C'
• You now have the location of three triangle vertices, the length of two sides, and the third side is easily calculable. It should be (relatively) easy to find the one missing angle.
• Angle 'b' is arctan({ΔY of "L"} / {ΔX of "L"})

EDIT: strikeout and added Angle 'b' calc

These found with: https://www.google.com/search?&q=find+intersection+of+line+and+circle
https://math.stackexchange.com/ques...intersections-of-a-straight-line-and-a-circle
https://www.mathportal.org/calculators/analytic-geometry/circle-line-intersection-calculator.php

These found with: https://www.google.com/search?&q=find+intersection+of+two+circles
https://math.stackexchange.com/ques...ind-the-points-at-which-two-circles-intersect
http://www.ambrsoft.com/TrigoCalc/Circles2/circle2intersection/CircleCircleIntersection.htm

Cheers,
Tom

 

[aleset]

thanks for answer.

I tried to calculate the angle "a". with trigonometry I have related the angle "b" with the angle "a". but I entered an swamp and I can not get out of it. in the sheet,

referred to the drawing, alpha = a, beta = b, x = c

 

[Tom.G]

I'm sorry. I misread the original problem. I solved for 'b' when 'a' is known, where you seem to want 'a' when 'b' is known.
I will have to think on that for a while.

Just to verify so I don't mess up again, are these known?

1. Crank radius 'r'
2. Connecting rod length 'L'
3. Offset of stroke path from crank center 'e'
4. Angle 'b'
5. Horizontal Position of left end of Connecting rod relative to crank center when 'b' is known

Tom

 

[Tom.G]

Think I've got it this time.

Per your initial drawing:
Find angle 'a'.

Knowns:

1. Rotational center of crank shaft
2. Crank radius 'r'
3. Connecting rod length 'L'
4. Path of stroke (centerline)
5. Angle 'b'

Solution:

• Using length 'L' and angle 'b', find the vertical location (Y co-ordinate) of the right end of right end of Connecting Rod 'L'
• Create a line, parallel to Stroke, that passes thru the right end of Connecting Rod 'L'
• Find the intersection of that line with the circle that describes the crank pin rotational path.
• That intersection defines the crank pin location.
• Angle 'a' is arctan({ΔY of "r"} / {ΔX of "r"}).
• With [ΔY, ΔX] being difference in locations of crank center of rotation and crank pin location.
  
  These found with: https://www.google.com/search?&q=find+intersection+of+line+and+circle
  https://math.stackexchange.com/ques...intersections-of-a-straight-line-and-a-circle
  https://www.mathportal.org/calculators/analytic-geometry/circle-line-intersection-calculator.php
  
  Cheers,
  Tom
  
  p.s. This woke me up two hours early this morning. Now I have to find two hours for the rest of my beauty sleep.

 

[JBA]

If you draw your figure with α = 90° you will see that another substitution for β is: asin ((r sin α) + e)/L) for solving for c based upon an input α value; but, cannot be reconfigured to solve for α based upon a c input value.

Edit: I have now realized something I should have seen earlier. You cannot have an equation to find an angle α from the stroke location c because there are two possible α angles in the crank rotation for anyone stroke distance c.=; as clearly illustrated in the below graph using sample L, r and e values for this problem.