Everything About the Degrees of Freedom of a Robot | Fundamentals of Robotics

Everything About the Degrees of Freedom of a Robot | Fundamentals of Robotics | Lesson 3

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Mecharithm - Robotics and Mechatronics

Күн бұрын

🌟 Contents 🌟
💎 (00:00) Introduction
💎 (00:48) Definition of Degrees of Freedom
💎 (01:28) Degrees of Freedom of a Rigid Body in a 3D Space
💎 (03:28) Degrees of Freedom of a Rigid Body in a 2D Space
💎 (05:09) Robot Joints Put Constraints on the Motion of the Robot Links Reducing Their Degrees of Freedom (dofs)
💎 (06:24) Degrees of Freedom (dofs) of a 3R Robot Arm
💎 (07:00) Types of Different Joints Used in Robots
💎 (07:13) Revolute (Rotary) Joints Provide One degree-of-freedom (DOF) for the Robot Links
💎 (07:47) Linear (sliding) Joints Provide One degree-of-freedom (DOF) for the Robot Links
💎 (08:07) Universal Joints (U) Provide Two Degrees of Freedom for the Links it Connects
💎 (08:24) Spherical Joints (S) Provide Three Degrees of Freedom Between the Connecting Links
💎 (08:49) Cylindrical Joints (C) Provide Two Degrees of Freedom Between the Connecting Links
💎 (09:02) Helical Joints (H) Provide One Degree of Freedom (DOF) Between the Rigid Bodies It Connects
💎 (09:39) Grübler's Formula to Find the Degrees of Freedom (DOFs) of Any Mechanism Including the Robots
💎 (11:16) Grübler's Formula for Two-Degree-of-Freedom (2-dof) Planar Robot Arm
💎 (12:11) Grübler's Formula for Four-Bar Linkage
💎 (13:27) Grübler's Formula for Stewart Platform
💎 (16:00) Grübler's Formula for Delta Robot
💎 (18:03) The problem of a 7 DOF Robot Arm Carrying a Tray with Drinks
In this video, you will learn ANYTHING that you've ever needed to know about the degrees of freedom (dofs) of a robot, and you will become familiarized with a general formula that you can find the degrees of freedom of any mechanism and not just robotic arms.
You can also read the whole lesson on our website:
🌐 www.mecharithm.com/degrees-of...
Be sure to also watch other lessons on Fundamentals of Robotics as some of the lessons are prerequisites for this lesson:
🔴 • Fundamentals of roboti...
🔴 • Configuration, and Con...
Thanks for watching! Ready to be a part of the Mecharithm family?👇
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🐦 / mecharithm
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References:
📘 Textbooks:
Modern Robotics: Mechanics, Planning, and Control by Frank Park and Kevin Lynch
A Mathematical Introduction to Robotic Manipulation by Murray, Lee, and Sastry
📹Videos:
- Four Main Types of Robotic Arm Geometry by Engineering Technology Simulation Learning Videos Channel:
• Four Main Types of Rob...
- Robot Joint Animation by Novanta Inc:
• Robot Joint Animation
- Cylindrical joint and Helical Joint from Keyan Ghazi-Zahedi's Channel:
• Cylindrical joint
• Helical Joint
- Honda's ASIMO robot carrying a tray:
• Closeup of Honda's ASI...
💲 If you enjoyed this video, please consider contributing to help us with our mission of making Robotics and Mechatronics available for everyone. We sincerely thank you for your generous contribution (you can do this by the Thanks button under the video).
©️ Tutorials and learning material are proprietary to Mecharithm, but sampling is permitted with proper attribution to the main source.
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Пікірлер: 79

@alexfish7792 4 ай бұрын

These videos are gold.

@mecharithm-robotics 4 ай бұрын

Thanks Alex. If you like to learn the same level of robotics but with some hands-on experiments using ROS2, you can also follow these lessons: github.com/madibabaiasl/modern-robotics-course/wiki they are basically the extended version of the videos but with more practice. note that although Dr. Madi used a physical robot in the lessons, she always explain that they can be done in the simulation as well (she shows how to do that in the lessons).

@alexfish7792 4 ай бұрын

@@mecharithm-robotics Thanks. By the way I'm actually not building robots. I'm doing game graphics programming. Requires a lot of rotation matrices and homogenous transformations. Maybe some day I'll get into robots :)

@mecharithm-robotics 4 ай бұрын

@@alexfish7792 that is a really cool application!

@thshm2938 10 ай бұрын

I've searched for many videos to understand DOFs, and this is by far the best explanation. Thankyou!

@mecharithm-robotics 10 ай бұрын

You are very welcome. Glad to help. This lesson can be accompanied by this lab: github.com/madibabaiasl/modern-robotics-I-course/wiki/Lab-5:-Exploring-DOFs-and-Joint-Types-in-the-PincherX-100-Robot-Arm-plus-DOFs-Practice-Questions Look at the other lessons in the GitHub wiki if you want to know how to setup the robot. Also, you can do everything in its simulation and you do not need the physical robot.

@lancecross9823 9 ай бұрын

You are a gift to the world. Very much appreciate your ability to teach.

@mecharithm-robotics 9 ай бұрын

you are very welcome!

@moldo800 Ай бұрын

Great video, Great explanation esepecially on Grubler's formula ps. I love it when Salma Hayek explains Mechanisms :D

@Chekuthan0101 5 ай бұрын

Fantastic video and explanation. Really appreciate showing proper examples for each DOF robot

@mecharithm-robotics 5 ай бұрын

you are most welcome. You can find more practical examples on the GitHub wiki: github.com/madibabaiasl/modern-robotics-course/wiki

@jimited1 Жыл бұрын

this was by far the best explanation! Thank you very much!

@mecharithm-robotics Жыл бұрын

you are very welcome!

@phonekeosiharath5452 Жыл бұрын

I'm in another class on this, but you do a much better job of explaining the ideas than the other professor. Much appreciated.

@mecharithm-robotics Жыл бұрын

You are most welcome!

@siddharthmaraje6987 2 жыл бұрын

Hello Madam, It would be great to mention in the video - which dofs are lost by the arm to avoid the spilling of drinks? The answer is of course - The roll motion of the wrist and the shoulder. Thus, having 5 dofs in the joint space (as you correctly said). But interestingly, the roll motion of the wrist and shoulder can compensate for each other by doing opposite motions. Thus, they can be allowed to move as well. For example, if the robot wants to place drinks in the middle of the table, then the elbow might collide with the table surface. In this case, equal and opposite roll motions of the wrist and the shoulder can help rotate the elbow sideways. So then, all joints move but the roll motion of the wrist and shoulder are coupled (they can't move independently without affecting each other). Can we then say that the effective reduction in the joint space dof is 1? Meaning there are 6 dofs allowed in the joint space? [wrist (yaw, pitch), shoulder (yaw, pitch), elbow (rotation), coupled roll of the wrist-shoulder = 6] I would like to know your opinion on this!

@ehsanmalekipour9988 3 жыл бұрын

Thanks for taking the time to make this video. Your effort to provide intelligible examples following each topic is admirable

@mecharithm-robotics 3 жыл бұрын

Thanks Ehsan for your Feedback; we do appreciate it.

@thshm2938 10 ай бұрын

Please also cover redundant DOFs, the condition where the Grübler's Formula must be modified.

@josehenriquemaia136 3 жыл бұрын

Thank you prof!!! the best explanation for introduction robotics! Um abraço do Brazil!

@mecharithm-robotics 3 жыл бұрын

Thank you Jose for your feedback.

@leandrogcosta 3 ай бұрын

Astounding

@TKNAVI 3 жыл бұрын

Really helped me grasp a concept that I was having a hard time with. Keep up the great content.

@mecharithm-robotics 3 жыл бұрын

Great to hear that. Currently working on a series of videos on all the tools needed to represent robot's motions: Configurations, velocities, and forces.

@ahmedsaad-hj6ey 3 жыл бұрын

You are the best. Thank you Prof

@mecharithm-robotics 3 жыл бұрын

Thank you for your feedback!

@CNsongs 2 жыл бұрын

Very good explanation. Thank you very much

@mecharithm-robotics 2 жыл бұрын

You are very welcome

@rajawadhwani8740 2 жыл бұрын

thank you, your lactures really helped me to grasp the conepts.

@mecharithm-robotics 2 жыл бұрын

You are very welcome. glad they helped.

@makesandmoocs8259 3 жыл бұрын

Very informative. Thankyou !

@mecharithm-robotics 3 жыл бұрын

Thank you for your feedback 🙏

@alexandrevalente9994 2 жыл бұрын

Now i see it clear. The Grubler’s formula is technically speaking not difficult to learn and apply. But these examples really give us a touch of what constraints are. Sometimes i have difficulties to count the dofs for individual joins, or is a bit tricky to understand how they mode in 3D space so I get wrong results when applying the formula.

@MrP-tking 3 жыл бұрын

Well explained. Subscribed.

@mecharithm-robotics 3 жыл бұрын

Thanks for your feedback.

@user-mh5hr4cb3o 3 жыл бұрын

Please continue with another episode Your explanation very nice 👌

@mecharithm-robotics 3 жыл бұрын

Thank you! We are working on big ones!

@sidhanth.m3054 2 жыл бұрын

Really helpful thanks a lot😊

@mecharithm-robotics 2 жыл бұрын

You are very welcome!

@mohitjoc25 3 жыл бұрын

Please keep posting more knowledge tutorials on robotics.... One day your channel really will be on top

@mecharithm-robotics 3 жыл бұрын

Thanks for your feedback and kind words Mohit!

@roger7341 Ай бұрын

The degrees of freedom (DOF) of any articulated mechanism is its mobility number, such as 0 or 1 or 2 or, etc. DOF is also the sum of all constrained joint mobility numbers. A kinematically locked joint has zero mobility or zero equivalent mechanical advantage, and a dextrous joint has nearly unity mobility and high equivalent mechanical advantage. The ith joint's mobility number may be obtained from the square of the norm of the ith row of the constraint Jacobian matrix's orthonormal null-space matrix. The number of columns in this matrix is DOF, as is its norm. The sum of squares of all row norms of this matrix is also DOF, which is why the sum of all joint mobility numbers is DOF. Technically a joint's mobility number is the square of the direction cosine between it and the mechanism's differential constraint manifold. Maximum motion and mobility is obtained when the joint is closely aligned with the manifold's surface, and minimum mobility when it is orthogonal to or nearly orthogonal to the surface. The most reliable way to get the correct DOF, which can also fail, is to apply Gaussian Elimination with Complete Pivoting (GECP) to a very accurate Jacobian matrix associated with the articulated mechanism's kinematic constraint equations. If the model has n variables and the Jacobian matrix has rank r, then DOF=n-r of the variables are independent. The wrong rank r and thus the wrong DOF may happen when mechanisms are over-constrained and some or all of the joints must be perfectly aligned to get any motion at all. At each stage of matrix factorization there is a remaining residual Schur complement matrix. When the norm of this matrix is zero or falls below some predetermined constant, the Schur complement matrix is considered to be zero and factorization stops. Matrix rank r is then the dimension of the resulting invertible factor matrices, not the number of rows or columns of the Jacobian matrix. Problems occur when the Jacobian matrix is noisy or in error for whatever reasons, and the noise or errors contaminate the remaining Schur complement matrix, causing the algorithm to incorrectly increase rank r and decrease DOF. Get the wrong DOF and the mechanism model will not perform as expected. A good example is a 6R Bricard mechanism with a 6 by 6 Jacobian matrix. When the six joints are laid out correctly and precisely the mechanism will have one DOF and articulate. Thus the matrix rank r must be 5, so DOF=6-5=1. But even tiny amounts of constraint error will lead to tiny amounts of error in the Jacobian matrix, and GECP will return a rank r=6 and DOF=0. Before factoring the Jacobian matrix to determine matrix rank and model DOF, the constraint violations must be minimized to the extent of available precision, and hopefully that will be enough for GECP to get the correct matrix rank and DOF. Incidentally, see what the Chebychev-Grübler-Kutzbach criterion is for this mechanism and ask yourself which method is more likely to be more accurate most of the time. See "Chebychev-Grübler-Kutzbach's criterion for mobility calculation of multi-loop mechanisms revisited via theory of linear transformations" by Grigore Gogu

@denisanisimov7036 2 жыл бұрын

Thanks for the video! It would be great if you also explain why do we actually care about the number of dofs? What's the use of it in practice? Where it leads us to?

@mecharithm-robotics 2 жыл бұрын

That is a great question, Denis. As an example, suppose that you are a robotics engineer and you are asked to design a robot with specific dofs that can perform a specific job (the task that a robot can perform depends on its dofs). Knowing about dofs, joints, links, and types of them is foundation knowledge that you should have before doing that.

@nikhiljoshi25 2 жыл бұрын

Thank you for creating this valuable series. The explanation is very precise and simplified. One small request. ..Would it be possible for you to put lecture numbers with the description which will enable us to view the videos in the correct sequence?

@mecharithm-robotics 2 жыл бұрын

Thanks for your comment. Sure, we can do that!

@kamyarothman8157 2 жыл бұрын

thank you actually I am working on motion planning of autonomous vehicles, and now I got to learn about C-space, could your please introduce a good reference that can help me in this case.

@mecharithm-robotics 2 жыл бұрын

have you watched kzfaq.info/get/bejne/d9mWeLymld_Rj6M.html? this video along with the text version provides a good insight into c-spaces.

@arkobiswas6303 Жыл бұрын

Nice video ma'am ! I have a little confusion regarding the last example. As you said we have to lock two dof of the wrist joint to avoid spilling, the same applies to shoulder joint, I believe. Further, the pitching dof of elbow should also be locked to avoid spilling. Please comment on these.

@srinjoykar7236 2 жыл бұрын

Thank You So Much mam ..... Your Teaching is better than engineering college professors

@mecharithm-robotics 2 жыл бұрын

Srinjoy, you are very welcome.

@preacher00000 3 жыл бұрын

Please make a video on 4bar mechanisms and inversions

@mecharithm-robotics 3 жыл бұрын

Thanks for your comment. We will incorporate it in future videos.

@fur7i236 2 жыл бұрын

how many degree of freedom for the arm robot holding the plate of glasses?

@mecharithm-robotics 2 жыл бұрын

fur7i, thanks for your question. As it is mentioned in the video, it will have 5 dofs. please refer to the video to know why.

@eng_nasurhasan7619 2 жыл бұрын

Excuse me are you can help me to answer my question A robot may be described as a redundant or not-redındant? Explain with two examples.

@mecharithm-robotics 2 жыл бұрын

Zoom zone, thanks for your comment. It's a great question. If a robot has more dofs than the task to perform, it is considered redundant. For instance, the human arm has 7 dofs, so if, say, it wants to manipulate a rigid object in space that has 6 dofs, then the human arm is redundant. Generally, if a robot's arm has more dofs than the dofs necessary to perform a task successfully, it's considered redundant.

@A.Hisham86 Ай бұрын

I didn't understand how a rotation and a translation in the same time compose one degree of freedom?

@mecharithm-robotics Ай бұрын

That's great question. Because in that specific joint, the motions are not independent of each other and happen at the same time thus having only 1DOF.

@turhancan97 3 жыл бұрын

First of all thank you for the video. I have a question. Can you please explain what exactly constraint means?

@mecharithm-robotics 3 жыл бұрын

Turhan, thanks for your comment. That's a great question. Think about the door hinge. As you saw in the video, a rigid body in space has 6 dofs but a door has only 1 dof. why? because the hinge restricted the body's movement and imposed 5 constraints on it thus it has only 1 dof (6-5). The same for a rotary joint for a robot. The joint imposed 5 constraints in space on the movement of the links and thus gives them only 1 degree of freedom. Hope this helped. Without a hinge or the joint, the rigid body (the door or the link of the robot) would've had 6 dofs in space.

@turhancan97 3 жыл бұрын

@@mecharithm-robotics Thank you so much for the explanation. You’re the best channel in robotics

@veyselkarani2282 2 жыл бұрын

Dear Dr. Babaiasl. It is great job for new generations. But I think you should check the replacement of X,Y,Z axes. Your video does not apply right hand rule in some stages.

@mecharithm-robotics 2 жыл бұрын

Veysel, thanks for your feedback. Would you please specify the timing? All coordinate frames are based on RHR. We would appreciate if you give the exact timing to check.

@veyselkarani2282 2 жыл бұрын

@@mecharithm-robotics one of them is at the 1.38, when you are showing X,Y,Z coordinates by the help of pipette. You say X by showing the blue pipette, Y by showing the red pipette, so on. That would be the mirroring effect of camera so I may be wrong. But I think so many audience did not realize. Second ; at the 2.14, You showed a coordinate system at the corner of a yellow cube. This coordinate system is not proper to RHR. You must exchange X and Y titles on the diagram.

@_JAINIK 2 жыл бұрын

I think the last example you gave of Asimov robot it should have 4 DOF and not 5. 3 translation and 1 rotation around z. Rest of the video was great.

@mecharithm-robotics 2 жыл бұрын

Jainik, thanks for your comment. From that point of view, yes but if you consider the robot arm to be a redundant manipulator with 7 dofs like the human arm then considering two constraints, it will have 5 dofs but you are also right if we consider the 6 dofs that a rigid body has in the space.

@roger7341 Ай бұрын

Are robots left-handed? Why are we using left-handed coordinate systems?

@shreyashsingh4468 3 жыл бұрын

first of all you are really cute .Mam I have problem in some questions please help me Question 1 : Can you please explain how the human hand has 7 degrees of freedom ( taking palm as a rigid body ) ? Question 2 : how the degree of freedom of n srs robotic arms holding a rigid body is n+6 ( n prismatic joint ,n spherical joint ) ? link of questions :muchensun.github.io/ModernRoboticsCourseNotes/ch2.html please help me mam i am stuck with these.

@mecharithm-robotics 3 жыл бұрын

Shreyash, thanks for your comment. Here are answers to your questions: Question 1: The shoulder is a ball and socket joint (refer to the spherical joint in the lesson) and it has 3 DOFs, the elbow has only one rotational DOF, and the wrist has 3 DOFs. Question 2: If you consider each of the open-chain arms as 7 DOFs (3 shoulder, 1 elbow, 3 wrist) that connects the object to the ground then we can say that: N = 2n + 1 (object) + 1 (ground) = 2n + 2 J = n(3 joints) = 3n Sigma f_i = n (3+1+3) = 7n then DOF = 6(2n+2-1-3n) + 7n = n+6 Note that they share the same object and that's why it has 2n links + 1 object + 1 ground

@shreyashsingh4468 3 жыл бұрын

@@mecharithm-robotics thank you mam 🥰

@haidershaker4430 3 жыл бұрын

I need report for 5 Degrees of freedom

@mecharithm-robotics 3 жыл бұрын

Can you elaborate on that? What do you mean you need a report for 5 dofs?

@haidershaker4430 3 жыл бұрын

@@mecharithm-robotics Choose a 5 degrees of freedom robot as you wish, then analyze the direct kinematics, reverse kinematics and speed analysis? That my question in exam

@mecharithm-robotics 3 жыл бұрын

@@haidershaker4430 Haider, thanks for your comment, unfortunately, we do not provide answers to exam questions but you are more than welcome to learn from the videos to solve them yourself.

@eastafricamedia7080 2 жыл бұрын

So beautiful gal😍😍😍

@eastafricamedia7080 2 жыл бұрын

I love u bbe

@alexandrevalente9994 2 жыл бұрын

Hello Madi, perhaps can you tell more about the « independence » in the degree of freedom ? It is something I don’t get fully. Thanks.

@mecharithm-robotics 2 жыл бұрын

Alexandre, thanks for your comment. In order for Grubler's formula to work, the constraints in the mechanism should be independent. We know that the constraints come from the joints. Now suppose a mechanism with a parallelogram structure with three links where each parallel link is connected to two joints. If you use Grubler's formula, you will get zero dofs for this mechanism which is a wrong answer since the mechanism can move and it is not rigid. The reason is that if you make any of the joints rigid, the movement of the other joints will also be affected and the mechanism cannot move. Therefore, the constraints (or the movement of the joints) are not independent of each other and we should be careful when using Grubler's formula. Any of the links with its two joints have no effect on the overall motion of this mechanism so when using Grubler's formula you should eliminate those to get the right answer.