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I used r6 and r7 vectors along the yellow boom to get from the bottom loops to the top one. I did not show this in the video since those vectors weren't in the loops, but you can use constraints of theta5 = theta6 and theta7 = theta8 to calculate the r6 and r7 vectors.

No, the ground only connects two links (input and output). The link order is just how many connection points it has, and the ground link has two connection points (both revolute joints).

We launched the water balloons from a bungee slingshot. Initial angle can be measured as the angle at which the slingshot is pulled back. To find initial velocity, use conservation of energy from cocked position to launch position and treat the bungee as a spring.

I give up

Yes, there are many possible correct vector loops. The direction of the arrows and what you name them generally does not matter, as long as the arrows go dot to dot between the joints and the equations match your diagram. See th-cam.com/video/1-HItSmJlc4/w-d-xo.html for more details.

@@dynamicsandkinematics ok, I've already watched this video, and two other examples videos, one of them contains more than one loop and I learned from it how to know how much loops that I need. but I need to be sure that I've got the idea. there are many different unknowns, and the equations I have, just about 2 or three. I cant solve it analytically!! I'm right?.

Most of the time, a mechanism with more than one loop is too complicated to solve analytically and must be done numerically. For a few cases, it is possible though.

@@dynamicsandkinematics good to hear that, can you confirm if my solution is right pls?

I can't verify correctness without seeing the problem and your solution

I have a Matlab Tutorials playlist here th-cam.com/play/PLTMo3nrl2KWbeCx8-OGfrMHcFOUSjyk4D.html that goes into solving vector loop equations and programming simulations, but I can certainly add more videos to it!

I can't calculate exactly without knowing the post-collision speed of at least one of the cars, but if it knocked you a block and a half, then just a reality check would say he must have been going way too fast.

It does not matter if the vectors go clockwise or counterclockwise as long as your equations match the diagram. The main rules are just go dot to dot. If there is a slider, include an arrow in its direction of motion, and whenever possible, follow ground.

@@dynamicsandkinematics ok thnks

You can use changing position vectors for the input. To calculate the unknown angles, you do need to use the Jacobian with Newton's method in a while loop. The easiest way to get the Jacobian is through velocity, but you can also just take partial derivatives or use the formulas explained in this video: th-cam.com/video/mBTLWPXTckU/w-d-xo.html . An example of using Newton's method to solve for unknown angles in code is here: th-cam.com/video/_Ikq9nQTrz4/w-d-xo.html

@@dynamicsandkinematics Thanks for the quick reply. I was thinking of using Gauss-Seidel to solve the set of equations, would that be possible?

Yes, any iterative method for solving systems of linear equations should work.

I can't send you the code, sorry. It is proprietary.

r9 is a stationary vertical vector pointing to where the slider begins. Then r10 is measured from that beginning point.

If the link rotates in the horizontal plane, then gravity does not come into the equation, and there is no potential energy change. So the PE part of the L equation would just be 0.

@@dynamicsandkinematics Okey means the equation L = KE? and I have another question if you want to help answer, some references use the linear KE equation 1/2 MV^2 for EoM on the Pendulum, in contrast to this video which uses KE Rotation, and in the case of the 1 DoF arm robot using both or KEt= KE Linear+KE Rotation, can you help explain which is the correct way?

Pure linear motion only works for a simple pendulum (point mass approximation). For the physical pendulum as in this example, or the 1-DOF robot arm example, the equation depends on the point you sum torques around. If you sum around mass center, use the KE linear + KE rotation equation. If you sum around the fixed point, use KE rotation. Since moment of inertia varies depending on the point you summed torques around, the final answer should be the same no matter which route you took.

@@dynamicsandkinematics if using the equation KE Rotation + KE Linear will produce the equation of motion for 1 DOF Link with two equations of inertia effects, namely Ml^2 θ"+Iθ". Are my results correct? I'm confused, actually Ml^2 θ" describes which part of the link inertia effect and Iθ" describes which part of the link inertia effect?

I don't quite understand your question. The total inertia can be found using the parallel axis theorem (rod inertia about center of mass combined with distance from origin), or simply for a rod about its end. Either way you should end up with the same answer.

You are correct. Not sure what happened there to get 70.7 deg. The formula is right but answer should be 57 deg.

The ends of the arrows must connect dot-to-dot, and if there is a slider, you need an arrow along it. Other than that, the direction of the arrows does not matter as long as your equations match what you drew. So you could draw all clockwise, or all counterclockwise, or a mixture.

This material is based on ch. 4 from: Design of Machinery: An Introduction to the Synthesis and Analysis of Mecha-nisms and Machines, R. L. Norton, McGraw-Hill, 2012, ISBN 978-0-07-352935-6 However, I am not very impressed with any kinematics books I have found, and I don't actually own a copy of the above. I based the video on notes from taking a kinematics course.

Yes! The subscripts are wrong but corrected at 6:50 The numbers are correct the whole time.

Matlab

Yes, you are correct. Thanks for the catch.

You're right. I accidentally used r = 0.2 m in my calculator.

Thanks! I love how dynamics relates to athletics.