   Jacobian matrix, ball joint
  Hello people,just playing a bit with inverse kinematics, but stumpled into a problem. The article I'm reading only covers setting up the jacobian matrix for 1DOF hinge joints and slider joints, but I'd really like to have some 3DOF ball joints too.For 1DOF joints, their entries in the matrix are calculated by ds_i / dtheta_j = v_j x (s_i - p_j)where s_i is the position of end effector i (I'm only using one though), p_j is the position of joint j, v_j is the hinge axis, and theta_j is the current rotation of the hinge.My limited mathematical understanding fails to see how more angles are stuffed into the above. I guess it's something with partial differentiations... But I'm a bit lost.Any pointers to where I can find some information about this? I tried googling, but I didn't manage to find anything useful. I'm probably going to buy a book later, but I want to play with it NOW! :)Thanks,Rasmus Neckelmann   
  Could you give a link to the article you are reading?   ;This article might be a little bit helpful; it has a section on creating a ball joint that goes into some detail.   ;  Here's the article: http://math.ucsd.edu/~sbuss/ResearchWeb/ikmethods/iksurvey.pdfomgomghilol: Yeah, I've read the ODE stuff, but couldn't really derive anything useful from it.   ;  It's been a little while since I touched on IK, but IIRC you can treat each DOF in a joint as multiple 1DOF joints.EDIT: btw, you can handle the ball joint with only 2DOF if you work in spherical polar coordinates.   ;  I actually don't understand this. A hinge removes 5 relative DOFs from the system and not just one. For inverse kinematics you usually use the pseudo inverse of the Jacobian (J*JT) to describe the system. I try to look at your paper to see if I understand what these guys are talking about. ;Quote:Original post by kadafAny pointers to where I can find some information about this? I tried googling, but I didn't manage to find anything useful. I'm probably going to buy a book later, but I want to play with it NOW! :)No need to buy a book, just download this one.  This is the most comprehensive book I've read regarding multi-body systems and the best bit is its absolutely free ^_^ ->http://mat21.etsii.upm.es/mbs/bookPDFs/bookGjB.htm   ;Quote:Original post by joanusdmentiaIt's been a little while since I touched on IK, but IIRC you can treat each DOF in a joint as multiple 1DOF joints.I've thought about that too, but my first intuition labelled it a hack :)I'll sit down and try some different things now.Quote:Original post by DonDickieDFor inverse kinematics you usually use the pseudo inverse of the Jacobian (J*JT) to describe the system.Well, the article I linked to earlier isn't particular fond of using the pseudo inverse for this. Among other things, it says it performs poorly near singularities (when arms are fully stretched out there'll be oscillation, etc). But, okay, maybe it's good enough for most practical purposes.Quote:MotorherpNo need to buy a book, just download this one. This is the most comprehensive book I've read regarding multi-body systems and the best bit is its absolutely free ^_^ ->http://mat21.etsii.upm.es/mbs/bookPDFs/bookGjB.htmWell, thanks for the link, it looks awesome :) I think I'm going to punish my poor roommate's printer with this.   