Talk:Forward kinematics

Revisions to this article
The kinematics equations of a robot are critical to its control. The same equations are used to generate computer animations of kinematic chains. Prof McCarthy (talk) 04:27, 15 January 2012 (UTC)


 * While I can understand your opinion on the importance parameter, the project is robotics, not robots. As such, kinematics as a whole are more than likely of high importance, this is simply part of that group and so has been assessed as mid-importance. Though anyone can change parameters it would be best to discuss with others first, especially the RObotics project.
 * Can you please ensure that your edits do not introduce bad grammar or prose, for example:
 * "The kinematics equations for serial chain robot are" - surely robots?
 * "The kinematics equations of the robot are used in robotics, computer games, and animation" - surely KE's of "the robot" are not used in computer games? "Kinematic equations are used in robotics, computer games, and animation." seems adequate for the information being conveyed to the reader.
 * The reverse kinematics explanation is confusing, it now reads almost identical to the KE explanation. I would suggest adding something which describes an intended position, rather than a specified position.
 * The original text included "orientation" of the end-effector, was this not true?

Perhaps most importantly:
 * Please explain why you changed the picture explanation from 7 DOF to 6 DOF?

Chaosdruid (talk) 19:27, 15 January 2012 (UTC)
 * Thank you for your note. I am sorry, normally I explain what I am doing when I make revisions.  I would be pleased to answer these questions.  This article and the one on inverse kinematics seemed so neglected both by editors and viewers that I did not realize that anyone would notice.  I will return shortly with an explanation. Prof McCarthy (talk) 20:37, 15 January 2012 (UTC)


 * Now regarding the picture of the robot which was originally labeled as having 7 degrees of freedom. I believe that most people familiar with robots would consider each of the cylindrical segments to represent a rotational degree of freedom.  There are six cylindrical segments, two that intersect to define the shoulder, one that forms the elbow, and three that intersect to form the spherical wrist, so the robot has six degrees of freedom.  This particular structure matches the kinematic structure often used to model an idealized PUMA manipulator.  Robots of this kinematic structure are given a seventh degree of freedom by inserting a rotational degree of freedom along the axis between the shoulder and the elbow.  I hope this helps. Prof McCarthy (talk) 23:44, 15 January 2012 (UTC)


 * Now regarding my bad grammar, I have no claim to excellence with grammar. I often make wording errors as I try to explain complex topics, so quite a number of my edits are an effort at clean-up of my own errors.  However, kinematics equations are used in things such as robots, computer games and animations, and yes the same basic kinematics equations are used in all three applications.  The word robotics refers to a field, and I suppose computer games and animation can be considered fields, so I see the potential for confusion.  With regard to the kinematics equations I do not claim to have the best descriptions, but I can say the an "intended position" is not the same as "specified position."  The critical issue is what is specified and what is computed.  In forward kinematics the joint angles are specified and the position of the end-effector is computed, and in inverse kinematics the position of the end-effector is specified and the joint angles are computed.  Finally, it is common to assume that the term position of a rigid body includes orientation.  I hope this helps. Prof McCarthy (talk) 23:58, 15 January 2012 (UTC)


 * The original label was 7 DOF and was taken from this "An articulated robot with 7 DOF in a kinematic chain (including surge at the end of the arm)." on Degrees_of_freedom_(engineering)
 * While I understand where your explanation comes from, I am a little confused. Chaosdruid (talk) 17:13, 17 January 2012 (UTC)


 * The six joints of the robot provide control of the six degrees of freedom of the end-effector as a rigid body. Those six degrees of freedom are described in the section on "degrees of freedom" in nautical terms, which is new to me, but not incorrect.  So the end-effector has three translational degrees of freedom, heaving, swaying and surging, and it has three degrees of freedom in orientation, roll, pitch and yaw.  I do not see an issue except for the miscount of seven when there are actually six joints in the robot.Prof McCarthy (talk) 19:09, 17 January 2012 (UTC)
 * Would rotation come into it? i.e. the rotation of the whole arm about the vertical axis? Chaosdruid (talk) 19:39, 17 January 2012 (UTC)
 * The first vertical cylinder provides this vertical rotation. The design of this robot is such that the first three joints combine to provide the three translational degrees of freedom of the end-effector. They position the wrist-center in space.  The axes of the three remaining joints intersect in this wrist-center and provide the roll, pitch and yaw orientation degrees of freedom.  This particular structure decouples the translation from the rotation, which simplifies the derivation of the inverse kinematics formulas.  This is an idealized version of the PUMA manipulator, because the actual PUMA manipulator has joint offsets that were necessary for packaging reasons that cause the first three joints to also impose orientation changes and the second three joints to also impose translation changes to the end-effector.  Is this what you are asking?Prof McCarthy (talk) 19:52, 17 January 2012 (UTC)
 * Nope, I wish it was otherwise, but I am still confused. Are we talking at crossed purposes? Is it that you are talking about how many DOF the end effector can act in, while I am talking about the arm's movements? Chaosdruid (talk) 06:37, 19 January 2012 (UTC)
 * Hmm...I guess I am providing too much information. If you want to focus on the arm's movement, that is fine.  The arm is a serial kinematic chain formed by seven links connected by six one degree of freedom joints, the cylinders shown in the illustration.  One of the links is the ground link that does not move.  The configuration of the chain relative to the ground link is controlled by the joint rotation angles around each of the six cylinders.  So the system has six degrees of freedom. Prof McCarthy (talk) 15:29, 19 January 2012 (UTC)
 * I am confident that you understand that a serial chain robot with six joints is a six degree of freedom robot, and further that a serial chain robot with seven joints has seven degrees of freedom. So I believe the only real question is does this figure show six or seven joints.  Thus, I assume you see seven joints where I see six.  I assign one joint per cylinder and there are six cylinders, thus I conclude that the figure shows a six degree of freedom robot.  It also happens to match the idealized kinematic structure of the popular PUMA robot.  I am sorry but I cannot see where or why you or others see a seventh joint. Prof McCarthy (talk) 16:05, 19 January 2012 (UTC)

Can you tell me what those six cylinders are please - I can see three. Two joined together by the blue plates, and one connecting the end effector to the arm. Ignoring those three, where are the other three? Chaosdruid (talk) 16:53, 19 January 2012 (UTC)
 * Ignoring the two parallel cylinders that form the upper arm, and the last cylinder that provides the last roll movement for spherical wrist, there is a vertical cylinder that is attached to the conical base, there is a cylinder that has colored stripes on it that forms the first roll joint in the spherical wrist, and there is a cylinder between two plates that provides the pitch movement in the spherical wrist. Prof McCarthy (talk) 17:04, 19 January 2012 (UTC)
 * Excellent! We are agreed so far... There is just this last "including surge at the end of the arm". Can we perhaps discuss what this may be referring to? THe only surge I can imagine it implies would be some movement on the tip of the end effector. Is this possible, or would that not normally be counted as a DOF? Chaosdruid (talk) 21:40, 19 January 2012 (UTC)
 * It is my understanding that surge refers to the foreword and backward translations in the rigid body movement of a ship. There is no joint that I am aware of that has movement that is described as a surge.  There are many ways to design an end-effector for a robot, but none that I have seen includes anything that would be described as a "surge."  Whoever miscounted the joints in this serial chain robot has also made a mistake in the reference to surge, which I can only assume refers to the six degree-of-freedom movement of the end-effector.  Finally, saying that a seventh joint exists when it is not shown in the figure seems odd to me.  Prof McCarthy (talk) 22:26, 19 January 2012 (UTC)


 * I notice that Chaosdruid has moved on to other subjects, so maybe we are done here. I believe the final conclusion can only be that someone misinterpreted this figure and identified seven joints.  My guess is that the stripes in the forearm were viewed by someone as denoting multiple joints, which is simply incorrect.  It is important to realize that a seven dof robot is non-standard and called a "redundant robot."  This is something that one would expect would have been identified by the creator of the drawing.  However, the original figure simply refers to this as a "3D model of robotic arm" which suggests the creator considered this to be a conventional robot which would have six dof.  It is interesting how errors like this become entrenched.  Prof McCarthy (talk) 11:54, 20 January 2012 (UTC)
 * Moved on to other subjects? What are you on about? This is wikipedia, you cannot expect people to reply or answer within 24, 48 or even 76 hours - real life sometimes takes precedent. Perhaps you have more time on your hands than others - then there is the time difference, I do not know if you realise it, but in some places it is night-time when for you it is the day.
 * It makes little difference to me whether this is redundant or not, and it is certainly not good to be inferring DOF from the image description - it would be akin to seeing a picture of a car and deciding if it was diesel or automatic from "A 3D model of our car". My main purpose here was to try and point out to you that you could perhaps do with more explanation for the general reader, l;ayman, non-technical editor - rather than write prose which is perhaps incomprehensible to the general reader. A secondary issue was the DOF being perhaps wrong, without you explaining satisfactorily why it is so. As yet you have simply said "because it is wrong" - there has only been our discussion, two people who do not agree and have not reached consensus. I am still not convinced that your explanation is correct, but more importantly that you are writing prose with the general reader in mind.
 * I have been coordinating the Robotics project for the last three years, copy-editing articles of all subjects for four and a half years, and for GOCE for a year and a half as well as being a GOCE coordinator for the last nine months, and I have 5,500+ pages on my watchlist. Do not make the mistake of assuming that someone has "moved on" simply because replies are not within your timeframe. Chaosdruid (talk) 22:00, 20 January 2012 (UTC)
 * I suppose I should be grateful that the Coordinator of the Guild of Copy Editors has devoted this effort to improve my prose for the general reader. I was under the mistaken impression that this was a discussion of the accuracy of the caption to a figure with someone familiar with robotics.  I now realize my mistake.  I do have one quibble, the comparison between a standard robot and a redundant robot is not at all similar to a comparison of a diesel versus gasoline engine.  The correct comparison would be to a car with one versus two engines, and certainly you can tell from an illustration whether a car has one or two engines.  And further the introduction of a second engine is significant enough that one would expect the creator of the illustration to comment on it.  Prof McCarthy (talk) 21:31, 22 January 2012 (UTC)
 * There is no need to get personal - your original comment was out of order, "moved on to...", I was showing you where my time is spent, so please do not turn it into something it was never intended to be, and certainly do not resort to a personal attack. You know full well that those comments about links on your personal talk page were me helping you and had nothing to do with copyediting or prose.
 * "The correct comparison", I believe you meant "in my opinion it is..."
 * I have not tried to discern anything from the image, I have rather tried to get you to explain why you changed it from the original caption - in other words I was asking why you thought your assumptions were more accurate.
 * I am beginning to think that perhaps you have more than one quibble, but let me put you straight. I am only concerned with avoiding WP:SYN, WP:OR and maintaining accuracy. It would be best for all if we can all try to do the same.
 * The encyclopaedia is for the general reader, not "someone familiar with robotics", hence the first part of the discussion; the caption is more to do with someone changing from the original has to show reasonable cause, the onus being on the person changing something to persuade consensus in favour of the change.
 * Finally, I suppose what we are looking at is "7 links with 6 DOF", according to your explanation? Chaosdruid (talk) 01:36, 23 January 2012 (UTC)
 * I am sorry if something I have written has appeared to be personal in some way, it was not my intent. From the beginning, I have tried to explain that a standard serial robot has six joints which give the robot six degrees of freedom.  This is not an assumption or an opinion, original research or a synthesis that advances a position, it is a design feature of a robot, similar to saying that a car has one engine.


 * The six joints allow the robot to position the three translation and three orientation degrees of freedom of the end-effector. If one assumes that each of the cylinders drawn by the creator of this figure denotes a one degree of freedom rotational joint, as is the usual practice in robotics texts, then this figure shows six cylinders which means it has six joints.  Such a robot is standard, in which case, the number seven in the caption is an error.   Because the figure shows six rather than seven elements that can be considered to be joints, it is reasonable to conclude that this is a six degree of freedom robot and that the number seven in the caption was an error.   Whether the caption should state that the robot has seven degrees of freedom or six degrees of freedom is not an issue of opinions, assumptions, original research or a synthesis that advances a position, it is a question of accuracy.


 * It is important to notice that if the robot did indeed have a seventh joint, the robot would require seven joint parameter values to position the six degrees of freedom of the end-effector. This is one more than usually appears in a robot, and therefore requires special handling in order to make the robot operate.  It could be considered to be similar to operating a car that has two engines rather than one.  This is not an opinion or assumption but a fact that arises from the presence of an extra actuator that positions then end-effector of the robot, similar to the presence of an extra engine that also positions the automobile.  Because of the significance of the additional joint, it is reasonable to look to the creator of the drawing for some indication of its presence, however there is nothing to suggest that this figure is anything other than a standard robot.


 * The statement in the caption that the degrees of freedom include a surge at the end-effector seems to be an attempt by someone to identify a seventh joint that is not shown in the figure. This attempt at a justification is flawed because surge does not refer to a joint movement but to one of the six degrees of freedom of the movement of the end-effector, thus the statement in the caption compounds the error.


 * I changed the captions so that a general reader would have the correct value for the degrees of freedom of the robot shown in the figure. This is not an opinion, assumption, original research or a synthesis that advances a position, instead it is an accurate description of a figure that has six cylinders depicting joints in a robot.  Prof McCarthy (talk) 05:17, 23 January 2012 (UTC)

Merge discussion
Looking at Forward kinematic animation and this page, it seems that the animation content could be rolled into a section here. However, I'm not familiar with the subject and hesitated to merge boldly, as there may be a good reason for having animation in its own article. -Xpctr8 (talk) 13:43, 13 July 2014 (UTC)
 * I think this is reasonable. The use of kinematics equations in animation is already part of the page on Inverse kinematics. Prof McCarthy (talk) 14:25, 13 July 2014 (UTC)

Done. The content from that page (under "Computer animation") could definitely use review by someone familiar with the subject. -Xpctr8 (talk) 01:29, 24 July 2014 (UTC)
 * When is the time to remove the merge templates? Prof McCarthy (talk) 05:32, 24 July 2014 (UTC)
 * Missed that when merging. Gone now. -Xpctr8 (talk) 12:44, 24 July 2014 (UTC)

Copying Content to Wikiversity
I am working on a course in robotics on Wikiversity and am copying content to that site: https://en.wikiversity.org/wiki/Robotic_Mechanics_and_Modeling/Kinematics#Footnotes Thank you. Admazzeo (talk) 15:23, 10 February 2020 (UTC)