# Calculating Rotation Angle in an Offset Slider-Crank Mechanism

• aleset
In summary, Tom has a offset slider crank mechanism. Of which he knows all the geometrical data, because he measures them. He does not understand how to calculate the rotation angle of the connecting rod knowing the stroke. In his formula, he has the angle b. He does not understand how to eliminate it from the formula. He tries to solve for the angle α using trigonometry, but enters an error. He finds the angle α using the equation given in the problem, where he knows the crank radius r, connecting rod length L, and offset of stroke path from crank center e.
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

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aleset said:
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##.

thanks thinch.

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

Wrong. See my posts 6 and 7, below.

1. Center of rotation of crank. Call this 'γ'
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

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

https://math.stackexchange.com/ques...ind-the-points-at-which-two-circles-intersect
http://www.ambrsoft.com/TrigoCalc/Circles2/circle2intersection/CircleCircleIntersection.htm

Cheers,
Tom

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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

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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?
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

Last edited:
Think I've got it this time.

Find angle 'a'.

Knowns:
1. Rotational center of crank shaft
3. Connecting rod length 'L'
4. Path of stroke (centerline)
5. Angle 'b'

Solution:

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.

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## 1. What is an offset slider-crank mechanism?

An offset slider-crank mechanism is a mechanical system that converts rotary motion into reciprocating motion. It consists of a crankshaft (rotary motion), a connecting rod (transfers the motion), and a slider (reciprocating motion). The main feature of this mechanism is the offset distance between the crank center and the slider center, which allows for a greater range of motion compared to a regular slider-crank mechanism.

## 2. How does an offset slider-crank mechanism work?

The offset slider-crank mechanism works by using the rotary motion of the crankshaft to transfer motion to the connecting rod, which then moves the slider in a reciprocating motion. The offset distance between the crank center and slider center allows for a greater range of motion, making it useful in applications such as engines and pumps.

## 3. What are the advantages of using an offset slider-crank mechanism?

Some advantages of using an offset slider-crank mechanism include its compact size, high efficiency, and ability to transmit high forces. It also allows for a smoother and more continuous motion compared to other types of mechanisms.

## 4. What are the applications of an offset slider-crank mechanism?

An offset slider-crank mechanism has a wide range of applications, including in internal combustion engines, pumps, compressors, and various types of machinery. It is also commonly used in automotive engines to convert the rotary motion of the engine's crankshaft into the reciprocating motion of the pistons.

## 5. How can the offset distance of a slider-crank mechanism be optimized?

The offset distance of a slider-crank mechanism can be optimized by considering the desired range of motion and force requirements. It is also important to consider the material and size of the components to ensure stability and efficiency. Advanced engineering techniques, such as computer simulations and prototyping, can also be used to optimize the offset distance for specific applications.

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