Problems in understanding kinematics

  • Thread starter arifle
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In summary: I am also confused with the translational and tangentianal velocities...In summary, tnich said that he is not sure why equation (8) in the first paper is multiplied by R(theta) again, and he is confused about translational and tangentianal velocities.
  • #1
arifle
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TL;DR Summary
wheeled robot kinematics and constraints
Hi, I tried to understand kinematics after having an omnidirectional roobt. Some problems stop me to go further. Here I upload some contents of different papers talking about kinematics. For the 1st three pictures, I don't know how equation (8) is from and I am little confused about translational and tangentianal velocities. I don't know why it mutiplys R(theta) again in equation (8).
66815456-dcb60900-ef6a-11e9-966b-2a5821ebff7e.jpg

66815457-dd4e9f80-ef6a-11e9-9469-29b2c29bf48d.jpg
66815458-dd4e9f80-ef6a-11e9-848a-4c41f34c2c68.jpg

For the 2nd paper, I cannot obtain the equation of v_trans,i. Also, I am not sure if the rotation matrix in this case is R(theta) = [cos(theta) -sin(theta); sin(theta) cos(theta)]. Can anyone please tell some details about the kinematics.
66815705-5948e780-ef6b-11e9-976c-843893a73e4d.jpg

At last, there is another lecture about kinematics. The problem is still about the constraints. How can I derive this pure rolling constraint.
QQ截图20191016114206.jpg
 
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  • #2
It looks to me as though equation (8) in the first paper is the dot product of the drive velocity with the direction vector of the drive's wheel, i.e. the component of the velocity in the direction of the wheel spins. I guess that would imply that the wheel is also sliding sideways. If ##\theta## is a function of time, then the extra multiplication by ##\mathbf R(\theta(t))## would give the direction of the wheel at time ##t##.
 
  • #3
tnich said:
It looks to me as though equation (8) in the first paper is the dot product of the drive velocity with the direction vector of the drive's wheel, i.e. the component of the velocity in the direction of the wheel spins. I guess that would imply that the wheel is also sliding sideways. If ##\theta## is a function of time, then the extra multiplication by ##\mathbf R(\theta(t))## would give the direction of the wheel at time ##t##.
Thank you, tnich. How can we get the equation of the rolling constraint if we focus on the 3rd approach.
 

Related to Problems in understanding kinematics

What is kinematics?

Kinematics is a branch of physics that studies the motion of objects without considering the forces that cause the motion.

What are the main problems in understanding kinematics?

The main problems in understanding kinematics include visualizing motion, interpreting graphs and equations, understanding vectors, and applying kinematic equations to real-world scenarios.

How can I improve my understanding of kinematics?

To improve your understanding of kinematics, it is important to practice solving problems and visualizing motion. It can also be helpful to use real-world examples and to seek clarification from a teacher or tutor if needed.

What is the difference between kinematics and dynamics?

Kinematics focuses on the motion of objects without considering the forces that cause the motion, while dynamics studies the relationship between motion and the forces that cause it.

What are some common misconceptions about kinematics?

Some common misconceptions about kinematics include thinking that acceleration and velocity are the same thing, believing that an object in motion must always have a constant speed, and assuming that direction is not important in describing motion.

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