tag:blogger.com,1999:blog-1409654809690469042.post4479110629057848377..comments2015-11-19T07:11:19.278-05:00Comments on I Heart Robotics: Stewart PlatformI Heart Roboticsnoreply@blogger.comBlogger3125tag:blogger.com,1999:blog-1409654809690469042.post-11169397443493027392009-06-30T14:06:13.099-04:002009-06-30T14:06:13.099-04:00"Well the idea is that mathematically theta a..."Well the idea is that mathematically theta and theta dot (rotational) or x and x dot (linear) would only be positive (ccw/fwd) or negative (cw/rev) but not both. This could have effect the results when solving inverse kinematics problems.<br />"<br /><br />If I got you right. The idea can be modeled by adding extra constraints to the equation group 1.<br /><br />equation group 1:<br />f1(x,y,z,alpha, beta, gama)= 0<br />f2(x,y,z,alpha,beta,gama)=0<br /><br />equation group 2:<br />f1(x,y,z,alpha, beta, gama)= 0<br />f2(x,y,z,alpha,beta,gama)=0<br />x>0<br />y>0<br />z>0<br />Diff(alpha)>0<br />Diff(beta)>0<br />Diff(gama)>0<br /><br />Does the equation group 2 have fractional numbers of free variables, thus fractional degree of freedom? <br /><br />I guess the "fractional degree of freedom" should be firstly defined in a mathematically describable fashion...hunn...fishkillhttp://www.blogger.com/profile/06851081589681302342noreply@blogger.comtag:blogger.com,1999:blog-1409654809690469042.post-3515514230683998782009-06-26T22:52:36.392-04:002009-06-26T22:52:36.392-04:00Well the idea is that mathematically theta and the...Well the idea is that mathematically theta and theta dot (rotational) or x and x dot (linear) would only be positive (ccw/fwd) or negative (cw/rev) but not both. This could have effect the results when solving inverse kinematics problems.<br /><br />I can't think of any chemical whose bonds can only be twisted or pulled in only one direction. It is usually assumed that translations and rotations are reversible, however a clutch and a <a href="http://en.wikipedia.org/wiki/Ratchet_(device)" rel="nofollow">rachet and pawl</a> are examples of devices that only rotate in only one direction.<br /><br />A car on the highway or an airplane would be examples of systems that can not linearly reverse direction.<br /><br />It appears that answer is probably related to <a rel="nofollow">Lie Algebra</a> and <a href="http://en.wikipedia.org/wiki/Holonomic#Robotics" rel="nofollow">Holonomic</a> motion.I Heart Roboticshttp://www.blogger.com/profile/12538673939219132671noreply@blogger.comtag:blogger.com,1999:blog-1409654809690469042.post-75408311852688364682009-06-26T12:35:53.425-04:002009-06-26T12:35:53.425-04:00In my opinion, "only move forward or only rot...In my opinion, "only move forward or only rotate clockwise" haven't been defined as a mathematical quantity, thus no good mathematical model can describe it consistently and simply. <br /><br />As far as I know, <br />A lot of system define degree of freedom as the NUMBER of free variables for equation of n variables, no matter the equation is physical chemistry equation or Quaternion or translation equation with x,y,z and Euler angles. The NUMBER of free variables can not be fractional.<br /><br />I think this is a fantastic question, because it challenged the limit of the existing mathematical model, you probably need to design your own mathematical system to describe the "fractional degree of freedom".Charleshttp://www.blogger.com/profile/06029572704560114734noreply@blogger.com