Modern Robotics, Chapter 2.1: Degrees of Freedom of a Rigid Body

This is a video supplement to the book "Modern Robotics: Mechanics, Planning, and Control," by Kevin Lynch and Frank Park, Cambridge University Press 2017. See modernrobotics.org for information on the book, free software, and other materials.
This video introduces the concepts of configuration, configuration space (C-space), and degrees of freedom, and describes a method for counting the degrees of freedom of a rigid-body in n dimensions.
This video is a brief summary of material from the book, and it is not meant to stand alone. For more details, such as an explanation of the notation, please consult the book and the other videos.
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Wiki for the book, including software and other supplements: modernrobotics.org
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[@user-cx3cv9vq3b]

this is some hardest way to explane DoF

[@parameciumcheese]

Thank you all for these videos! I'm so excited that you all have put so much effort into making this information available with the book and such. Thanks.

[@sachinfulsunge9977]

Thought this was going to be beginner friendly

[@insertusername5737]

I didn't understand almost anything and now i'm now more confused than ever, thank you for that :S
Thanks for all the content, but without examples it's hard to understand. Why two-joint can be shown as a torus exactly? Show it with an example, because without that for a beginner is just like nothing, it can mean anything. And why suddenly two points on a rigid body can be transformed to 2 spheres with a (circle?) between? Why you suddenly added a C point?
Seriously, this is incredibly confusing. Take it as a good advice anyways

[@RohanKumar-oz8tc]

Thanks for the video. I didn't understand how when specifying C, we have moved B away from the circumference of the point A. Isn't B supposed to be at the circumference of A?

[@user-pg6py8wv3m]

thank you mister . its helpful

[@paramitapal392]

Consider a joint between two rigid bodies. Each rigid body has mm degrees of freedom (m=3m=3 for a planar rigid body and m=6m=6 for a spatial rigid body) in the absence of any constraints. The joint has ff degrees of freedom (e.g., f=1f=1 for a revolute joint or f=3f=3 for a spherical joint). How many constraints does the joint place on the motion of one rigid body relative to the other? Write your answer as a mathematical expression in terms of m and f. ans?

[@thakervedant3170]

here the Answer is m-f.
as per the equation given over here, f+c=m . and we want the value of c in terms of m and f.

[@logicraju]

Can't understand 1:46. The CSpace should be a disk, right? How come it became a torus?

[@rajatsharma6137]

u r right....i guess the first joint is orthogonal to the second...he has mistaken it...it should actually be an annular disc...

[@mccunnj]

It is the result of S1xS1. 1 Joint rotation is the angle on the torus from above, and the second is the angle within the torus itself.

[@goktugguvercin8069]

In the video, it is said that there is only one number needed to specify location of point C. I could not understand it. How can we specify location of point C with one value ?

[@sparshmecwan2962]

See the location of point C is represented by 3 numbers but it's position has to be in the circle that A and B formed which means it has to be at a particular distance from A and B ,and whatever the position might be in that circle, it IS going to be represented by 3 coordinates. It's not the coordinates of point C that is decreasing, its the degrees freedom of it's location.
Edit: I'm replying 7 months later, you probably would have mastered robotics until now. xD

[@rajatsharma6137]

a circle is parametrically represented with just theta...any curve is intrinsically one dimensional..

[@sidharthsaratrajbatchu6593]

​@@sparshmecwan2962 but still your answer is helping me with same question
But professor mentions point c wrt a as an outer parameter of the B sphere

[@charismaticaazim]

Simply take any object (e.g. pen, shoe) & fix its x & y co-ordinates (i.e. keep it constant), then you'll observe that you only need one more number to specify the location of the object.

[@hichemsetif1741]

hey nice video ,can you do a video for 5 DOF bipedal robot .thanks
if have one send me the link.

[@Luhpu]

شرح صعب جدا وغيرمفهوم