Design a Crank Mechanism: Solutions & Equations

In summary, the conversation is discussing the design of a crank mechanism and the calculation of the piston position. The equation being discussed is l^2 = r^2 + x^2 - 2*r*x*cos(A), which is used to calculate the position of the center of the piston wrist pin. The total stroke is 2*r and the position of the piston can be calculated using a perpendicular from the stroke line and the angle A.
  • #1
I want to design a crank mechanism. I found this page on Wikipedia
https://en.wikipedia.org/wiki/Piston_motion_equations

500px-Piston_motion_geometry.png


Relating from this diagram, is x the max stroke of the piston ?, or is it PO-(max stroke of piston) ?

And why is l^2 = r^2 + x^2 - 2*r*x*cos(A)

Shouldn't it be, l^2 = r^2 + OP^2 - 2*r*OP*cos(A) ?
 
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  • #2
Total stroke is 2*r. There are a couple of ways to calculate piston position (the position of the center of the piston wrist pin, to be more precise). A common one is to use a perpendicular from the stroke line to form two right triangles. The length of that perpendicular is r*sin A. So the piston is at (r*cos A) + [l^2-(r*sin a)^2]^0.5. When angle A is zero the position is (l+x). When angle A is 180 deg the position is (l-x).

If you look further down in the Wikipedia article you will find the equation above.
 
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1. What is a crank mechanism?

A crank mechanism is a mechanical device that converts rotary motion into reciprocating motion. It consists of a crank, connecting rod, and a piston. The crank rotates to create a reciprocating motion in the connecting rod, which in turn moves the piston back and forth.

2. What are the components of a crank mechanism?

The main components of a crank mechanism include a crank, connecting rod, and a piston. The crank is a lever arm that rotates to create motion. The connecting rod connects the crank to the piston, which moves back and forth in a straight line. Other components may include bearings, seals, and lubrication systems.

3. What factors should be considered when designing a crank mechanism?

When designing a crank mechanism, factors such as the intended purpose, load capacity, speed, and accuracy must be taken into consideration. The size and shape of the components, as well as the type of materials used, also play a crucial role in the design process. It is important to ensure that the mechanism is durable, efficient, and meets the desired specifications.

4. What equations are used to calculate the motion of a crank mechanism?

The equations used to calculate the motion of a crank mechanism include the crank radius, connecting rod length, and the angle of rotation. The equation for the displacement of the piston is given by: y = R(1-cos(theta)) + L(sqrt(1-sin(theta)^2)). The velocity and acceleration of the piston can also be calculated using derivatives of this equation.

5. What are some common applications of crank mechanisms?

Crank mechanisms have a wide range of applications in various industries, including automotive, aerospace, and manufacturing. They are commonly used in engines, pumps, compressors, and other machines that require rotary-to-reciprocating motion. Crank mechanisms are also used in bicycles, hand tools, and other mechanical devices.

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