4 Linkage system: velocity calculation

In summary, a 4 linkage system is a mechanical system with four interconnected rigid bars or links used to convert input motion into desired output motion. Velocity in a 4 linkage system is calculated using the instantaneous velocity method, which can be affected by factors such as link length and angle, joint location, and external forces. The velocity of a 4 linkage system can be changed by adjusting these factors or by altering the speed or adding links. Practical applications of a 4 linkage system include machinery, robotics, and automotive engineering for efficient and accurate movement.
  • #1
vsarnaud
2
1
Homework Statement
I want to calculate the x-vector velocity of the middle leg of the walking machine. This requires two angular velocities. The one from the leg (which I've calculated), and the one from the driver (which I've set to a value, see below).

I can't seem to figure out what the total velocity of this leg is. The program shows me a value (see below) but I can't seem to find an appropriate formula to add both angular velocities together.
Relevant Equations
You could compare this problem to a trebuchet, golfswing or a folded arm that stretches. Where you have two seperate angular velocities resulting in one larger angular velocity.

R1 - R2 - R3 - R4 = 0 (see screenshots)
For the attempt at a solution view the Excel screenshots (1).

A screenshot with all the lengths is provided (2).

The 4-linkage system is shown in screenshot (3).

The problem is shown in screenshot (4).

A screenshot from the whole assembly is also provided to add some insights (5).

Thanks for the help!

(I did not create this 3D model, I chose this project to do calculations for one of my lectures)
 

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  • #2
Nevermind... I accidently entered the value for θ4 = 0°, but it is equal to 90°...

Sorry for wasting time! :oops:

Kind regards!
 
  • Like
Likes Tom.G

1. What is a 4 linkage system?

A 4 linkage system is a mechanical system consisting of four rigid bodies connected by joints or links. The motion of one body affects the motion of the other bodies in the system.

2. How is velocity calculated in a 4 linkage system?

Velocity in a 4 linkage system is calculated using the principle of conservation of angular momentum. This means that the sum of the angular velocities of all the bodies in the system is equal to zero.

3. What factors affect the velocity in a 4 linkage system?

The velocity in a 4 linkage system is affected by the length and orientation of each link, the position and direction of the joints, and the speed and direction of the input motion.

4. Can the velocity in a 4 linkage system be controlled?

Yes, the velocity in a 4 linkage system can be controlled by adjusting the length and orientation of the links, as well as the position and direction of the joints. Additionally, the speed and direction of the input motion can also be controlled.

5. What are some real-world applications of 4 linkage systems?

4 linkage systems are commonly used in robotics and mechanical engineering to create complex movements and motions. They can also be found in various machines and equipment, such as car suspensions, cranes, and even in the human body (e.g. the knee joint).

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