Right triangle with four jointed links

In summary, the discussion involves finding the height (x) of a right triangle ABCD formed by four jointed links, with joint D being pushed to the midpoint of the hypotenuse to lie on leg AB. The given equation for finding x is (2a)2 = a2 + x2, which simplifies to x = √3 * a. The next step is to find the angle DCB and note that the new, smaller triangle is isosceles. Using the fact that the altitude from C bisects angle DCB and creates two new right-triangles, there is a relation between angle, height, and hypotenuse. The final solution involves finding the length of DB, which is
  • #1
chawki
506
0

Homework Statement


A right triangle ABCD is formed from four jointed links. The joint D at the midpoint of the hypotenuse is pushed until it lies on the leg AB.

Homework Equations


Find the height x when a = 50 mm

The Attempt at a Solution


give me a hint please cause I'm lost :mad:
 

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  • #2
Well, if I was given a right triangle and the length of two of the sides, I would first find out what the length of the third side is, Pythagoras.
 
  • #3
ok, let the distance AB=x

(2a)2=a2+x2
x2= 4a2-a2=3a2
x=[tex]\sqrt{}3[/tex] * a
x=86.60mm
and then DB=86.60-50
DB=36.6mm.

But then?
 
  • #4
I would find the angle DCB using the initial right triangle, then note that the new, smaller triangle is isosceles because DC=(2a)/2 and CB=a. Then use the fact that the altitude from C bisects angle DCB and creates two new right-triangles...you then have a relation between angle, height, and hypotenuse.
 
  • #5
sounds complicated!
 
  • #6
How can we find the angle DCB ?
 
  • #7
Apphysicist said:
I would find the angle DCB using the initial right triangle, then note that the new, smaller triangle is isosceles because DC=(2a)/2 and CB=a. Then use the fact that the altitude from C bisects angle DCB and creates two new right-triangles...you then have a relation between angle, height, and hypotenuse.

hello
 
  • #8
AB-a=86.6-50=36.6mm

now, a2=x2+(36.6/2)2
x=46.53mm ?
 

1. What is a right triangle with four jointed links?

A right triangle with four jointed links, also known as a four-bar linkage or a four-bar mechanism, is a mechanical system consisting of four rigid bars connected by four joints. It is commonly used in engineering to convert rotational motion into translational motion or vice versa.

2. How does a right triangle with four jointed links work?

A right triangle with four jointed links works by utilizing the principles of kinematics and mechanical advantage. As one bar rotates, the other three bars move in a coordinated manner due to the constraints of the joints, allowing for controlled motion and force transmission.

3. What are the applications of a right triangle with four jointed links?

A right triangle with four jointed links has a wide range of applications, including in machines, vehicles, robotics, and even in the human body (such as the knee joint). It can be used to create different types of motion, such as linear, rotary, or oscillating, and can also be used for force amplification and precision movement.

4. What are the advantages of using a right triangle with four jointed links?

One of the main advantages of a right triangle with four jointed links is its simplicity in design and construction. It is also highly versatile and can be used for various purposes, making it a commonly used mechanism in engineering. Additionally, it allows for precise control of motion and force, making it suitable for applications requiring accuracy.

5. What are the limitations of a right triangle with four jointed links?

While a right triangle with four jointed links has many advantages, it also has some limitations. For example, it can only create a limited range of motion and may not be suitable for applications requiring complex movements. It also requires careful design and calibration to ensure smooth operation and avoid potential issues such as jamming or excessive wear of the joints.

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