# Mechanism Geometry: Solving a Fixed Point Problem

• Kalus
In summary, the problem involves a slider crank with fixed points A and B and a rotating beam labeled 20. The aim is to find the degree of rotation of the beam fixed at A in response to the 40-degree rotation of the 20-long beam. A possible solution involves using the pythagorean theorem for non-right angles and making calculations with the triangles ACB, CBD, ACD, and ADB. This will result in 3 equations and 4 unknown angles, which can be solved to find the rotation of the beam fixed at A.
Kalus
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

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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## 1. What is a fixed point problem in mechanism geometry?

A fixed point problem in mechanism geometry involves finding the fixed point or stationary position where all points on a mechanism remain in the same position relative to each other. This is important in designing efficient and functional mechanisms.

## 2. How is a fixed point problem solved in mechanism geometry?

There are various methods for solving a fixed point problem in mechanism geometry, including graphical methods, analytical methods, and numerical methods. The most commonly used method is the graphical method, where the mechanism is drawn and the fixed point is determined by visual inspection.

## 3. What are some common applications of solving fixed point problems in mechanism geometry?

Fixed point problems in mechanism geometry have many applications in different fields, such as mechanical engineering, robotics, and computer graphics. They are used to design and analyze various mechanisms, such as linkages, gears, and robotic arms.

## 4. What are the challenges involved in solving fixed point problems in mechanism geometry?

The main challenge in solving fixed point problems in mechanism geometry is to ensure that all the points on the mechanism remain in the same position relative to each other. This can be difficult to achieve due to factors such as friction, wear and tear, and external forces.

## 5. How important is it to accurately solve fixed point problems in mechanism geometry?

Accurately solving fixed point problems in mechanism geometry is crucial in designing efficient and functional mechanisms. A small error in the fixed point can result in significant issues in the overall performance of the mechanism, leading to safety concerns and decreased efficiency.

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