Understanding Vector Loops 1

[Tophinater]

I'm trying to create some models based on vector loops. However this a new concept for me and Im having a hard time finding a lot of imformation about it. Has anyone here used vector loops before and can point me in the direction of a website, reference, or possibly give me a quick summary of what they are?

 

[jistre]

I assume you're talking about kinematics task where you're trying to analyze or design some sort of linkage or mechanism, but there's no really "quick" summary.

In essence, you model a mechanism by defining each link as its pin to pin distance and then some angle, getting a vector. A deterministic mechanism should always be able to be defined such that the total of all the positional vectors add up to zero. Picture a parallelogram mechanism. Hold one leg fixed in space and call it the ground link. Start at one end of the ground link and move clockwise around the mechanism. Each link defines a vector (length and angular position), but if you trace all four of these vectors, you end up back where you started, no matter what position the three links that are free to move are in. This is what is meant by a vector loop. The total displacement around the loop is always zero.

The power of this is that you can write this vector equation out. Once you have this equation, then you work to get everything defined in the terms of one unknown, perhaps a crank angle or a slider position. At this point, you can get the position of any of the pins if you're given the crank angle, so you can trace out the motion of each pin versus crank angle.

In addition, you can differentiate the position vector loop, and it becomes a velocity vector loop, allowing you to calculate the velocity at each pin. Differentiate again, and you can calculate the acceleration of each pin. One more time, and you get the jerk at each pin.

It's a pretty involved and mathematical concept, but extremely powerful if you are designing mechanisms. For a reference, check out the McGraw Hill machine design series. I believe they even have one text that covers nothing but kinematics of mechanisms. That should give you everything you'd ever want to know about vector loops.

 

[ietech]

Here is an interesting website, hope it helps

http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html

 

[Tophinater]

Thanks for the replies, thats exactly what I needed to know. My original thought of vector loops is exactly what jistre described but doing some research I found something different when it was replated to cardiac modeling of the heart and arteries. Yes I am using it to develop a kinematic mechanism, more of a path for one really.

 

[tygerdawg]

Sounds like your basic Sophomore-level Machine Design & Kinematics class about four-bar linkage analysis. I did a quick Google and there's lots of info for that.

Here's a clever one:

http://www.softintegration.com/chhtml/toolkit/mechanism/fourbar/posvelaccelPlot.html

TygerDawg
Blue Technik LLC
Advanced Robotics & Automation Engineering

http://www.bluetechnik.com

 

[MechanicalChef]

Four-bar linkages were the bane of my existence for one semester of my life.