From: dwells@nrao.edu (Don Wells) Newsgroups: sci.math.num-analysis Subject: Re: Freebody problem Date: 25 Dec 1996 20:31:57 GMT Mike McDermott <100447.764@CompuServe.COM> wrote: >> I need to solve the equations of motion of a 3 dimensional free >> body, >> eg a tetrahedron, positively located by a total of six links from >> its >> vertices to six fixed points. Any ideas, references, etc? It has >> been >> applied to the platform of a flight simulator, so numerical >> solutions must be known, but I can't find anything >> published in that area. This type of system is often called a Stewart(sp?) Platform. There is an extensive literature on the subject, as you guessed, primarily in areas of robotics and precision machine tool control. I am at home, so I can't include sample citations in this followup. The problem is solved by starting from the desired orientation of the platform and solving for the actuator lengths. I.e., tilt and translate the platform, get the new coordinates of the U-joint connection points and compute the distances from those points to the fixed U-joint points at the other end of the actuators; these distances give you the lengths to command to get the desired platform orientation. If you need to solve the problem in the other (backward) direction, i.e. to get the platform orietation for a set of 6 lengths, you find it by Newton-Raphson iterative numerical inversion of the "forward" algorithm. It appears that, in many (most? all?) practical cases, you don't need to compute the partial derivatives for each iteration, that you can, in fact, use derivatives for the "home" positional of the platform. I implemented such a solution for control of an ellipsoidal mirror 8 meters in diameter which is moved by six actuators. See: ftp://fits.cv.nrao.edu/pub/gbt_actuators.tar.gz -- Donald C. Wells Associate Scientist dwells@nrao.edu http://fits.cv.nrao.edu/~dwells National Radio Astronomy Observatory +1-804-296-0277 520 Edgemont Road, Charlottesville, Virginia 22903-2475 USA