Yes, exactly, its the linear bearings that can be at different locations and force therefore the board to different positions, those are the ones that i am interested in!
On Saturday, June 11, 2016 at 6:49:34 PM UTC+2, Jason Moore wrote: > > If the blue dots are fixed on the board, doesn't the linear bearings > remove all degrees of freedom? I don't see how this thing can move. > > > Jason > moorepants.info > +01 530-601-9791 > > On Sat, Jun 11, 2016 at 8:57 AM, <[email protected] <javascript:>> > wrote: > >> They describe the location of the board (the blue rectangle) in relation >> to its "normal" position by a rotation about an angle of phi and a >> translation of x and y. >> >> >> >> On Saturday, June 11, 2016 at 5:40:26 PM UTC+2, Jason Moore wrote: >>> >>> Where are phi, x, y on the diagram? >>> >>> >>> Jason >>> moorepants.info >>> +01 530-601-9791 >>> >>> On Sat, Jun 11, 2016 at 6:35 AM, <[email protected]> wrote: >>> >>>> I guess its hard to get from my description, so i uploaded a drawing to >>>> visualize the physical problem: http://pasteboard.co/1Bvt53hY.png >>>> >>>> Thanks for your interest! >>>> >>>> >>>> >>>> On Saturday, June 11, 2016 at 3:13:52 PM UTC+2, [email protected] >>>> wrote: >>>>> >>>>> >>>>> Physically, the rows of A are three points fixed on a movable board. >>>>> >>>>> These points run freely in three linear bearings which are placed on a >>>>> fixed base. >>>>> >>>>> The linear bearings are described in hesse normal form in the rows of >>>>> matrix C. >>>>> >>>>> The robust motion matrix B is the transformation which transforms >>>>> points on the board to points in the base. >>>>> >>>>> So together my constraint D = (A * B) * C means >>>>> - Transform the points in A from the board to the base: A * B >>>>> - Compute the distance from the linear bearings: * C >>>>> - Claim that the distances are zero and solve for the motion >>>>> >>>>> I am aware that there are some other approaches to tackle this >>>>> problem, but i was not able to get a grip on them such that i could >>>>> formulate them in code. >>>>> >>>>> >>>>> >>>>> On Saturday, June 11, 2016 at 1:50:25 PM UTC+2, brombo wrote: >>>>>> >>>>>> Physically what are all the matrices. Do A and C also describe >>>>>> rotations. Please give the actual physics problem as well as the >>>>>> resulting >>>>>> math. >>>>>> >>>>>> On Sat, Jun 11, 2016 at 6:37 AM, <[email protected]> wrote: >>>>>> >>>>>>> My description was a little compressed, so i had to clean up the >>>>>>> code to match my description again ... >>>>>>> The code is available here: http://pastebin.com/MMW3B88h >>>>>>> I hope its readable for you. >>>>>>> >>>>>>> >>>>>>> >>>>>>> Am Donnerstag, 9. Juni 2016 20:24:35 UTC+2 schrieb Jason Moore: >>>>>>>> >>>>>>>> Can you please share the code so we can see what you are doing? >>>>>>>> >>>>>>>> >>>>>>>> Jason >>>>>>>> moorepants.info >>>>>>>> +01 530-601-9791 >>>>>>>> >>>>>>>> On Wed, Jun 8, 2016 at 11:58 PM, <[email protected]> wrote: >>>>>>>> >>>>>>>>> I am trying to solve a system of equations with sympy that arises >>>>>>>>> from a constraint of the form: >>>>>>>>> >>>>>>>>> (A x B) x C = D >>>>>>>>> >>>>>>>>> where >>>>>>>>> >>>>>>>>> * A, B, C and D are 3x3 matrices >>>>>>>>> * the diagonal of D should be zero >>>>>>>>> * B is a "rigid motion 2D" transformation, with elements cos(phi), >>>>>>>>> +-sin(phi), x and y >>>>>>>>> * A and C are fully filled with (supposedly known) values >>>>>>>>> * I want to solve for phi, x and y >>>>>>>>> >>>>>>>>> This gives me four equations: >>>>>>>>> >>>>>>>>> * one for each diagonal element in D >>>>>>>>> * one additional (quadratic) equation sin^2(phi) + cos^2(phi) = 1 >>>>>>>>> >>>>>>>>> When feeding those to equations directly to sympy, this takes some >>>>>>>>> hours and then breaks with an out of memory message. >>>>>>>>> >>>>>>>>> My next approach was to help sympy by guiding the solution step by >>>>>>>>> step (*). >>>>>>>>> >>>>>>>>> * First i took two of the linear equations and let sympy solve for >>>>>>>>> x and y (works great) >>>>>>>>> * Instead of having cos(phi) and sin(phi) in the B matrix, i >>>>>>>>> introduced new symbols cosphi and sinphi >>>>>>>>> * Then i took the resulting expressions for x and y, and solve >>>>>>>>> with the third linear equation for the cosphi element (works too) >>>>>>>>> * Finally i tried to solve the quadratic equation for sinphi by >>>>>>>>> inserting the just gathered cosphi expression >>>>>>>>> * The last step was not feasible without transforming the >>>>>>>>> expression to a polynom in sinphi and by replacing all coefficient >>>>>>>>> expressions by new symbols, then it worked >>>>>>>>> >>>>>>>>> The resulting expressions for x, y and phi (written as python >>>>>>>>> expressions) are about 3 MB (!) of text. >>>>>>>>> >>>>>>>>> This does not seem to be adequate to the problem, and when >>>>>>>>> converting to a theano function i get "maximum recursion depth >>>>>>>>> exceeded". >>>>>>>>> When i look at the expressions they are very repetitive, so i >>>>>>>>> tried CSE, which brings it down to about 30 KB, but they are still >>>>>>>>> very >>>>>>>>> repetitive and full of patterns. >>>>>>>>> >>>>>>>>> I suspect that the resulting expressions actually just perform >>>>>>>>> some matrix operations, so probably there would be an efficient way >>>>>>>>> to >>>>>>>>> compute the solution if only one could get back to matrix expressions. >>>>>>>>> I tried to guess what the appropriate matrix operations are, but >>>>>>>>> without success (**). And this feels of course very wrong and >>>>>>>>> backwards. >>>>>>>>> >>>>>>>>> Is there some obvious approach to such problems that i missed? Is >>>>>>>>> the problem actually that hard? >>>>>>>>> >>>>>>>>> I am aiming for a mostly automated solution process without steps >>>>>>>>> like (*) and (**), because i have a hand full of very similar >>>>>>>>> problems >>>>>>>>> ahead ... >>>>>>>>> Any hint appreciated! >>>>>>>>> >>>>>>>>> -- >>>>>>>>> Best regards >>>>>>>>> Janosch >>>>>>>>> >>>>>>>>> -- >>>>>>>>> You received this message because you are subscribed to the Google >>>>>>>>> Groups "sympy" group. >>>>>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>>>>> send an email to [email protected]. >>>>>>>>> To post to this group, send email to [email protected]. >>>>>>>>> Visit this group at https://groups.google.com/group/sympy. >>>>>>>>> To view this discussion on the web visit >>>>>>>>> https://groups.google.com/d/msgid/sympy/8555837f-d87d-484c-b882-2d8f7085d3b2%40googlegroups.com >>>>>>>>> >>>>>>>>> <https://groups.google.com/d/msgid/sympy/8555837f-d87d-484c-b882-2d8f7085d3b2%40googlegroups.com?utm_medium=email&utm_source=footer> >>>>>>>>> . >>>>>>>>> For more options, visit https://groups.google.com/d/optout. >>>>>>>>> >>>>>>>> >>>>>>>> -- >>>>>>> You received this message because you are subscribed to the Google >>>>>>> Groups "sympy" group. >>>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>>> send an email to [email protected]. >>>>>>> To post to this group, send email to [email protected]. >>>>>>> Visit this group at https://groups.google.com/group/sympy. >>>>>>> To view this discussion on the web visit >>>>>>> https://groups.google.com/d/msgid/sympy/ccde273d-ee0e-46bc-a822-7d1b9ff88f7e%40googlegroups.com >>>>>>> >>>>>>> <https://groups.google.com/d/msgid/sympy/ccde273d-ee0e-46bc-a822-7d1b9ff88f7e%40googlegroups.com?utm_medium=email&utm_source=footer> >>>>>>> . >>>>>>> For more options, visit https://groups.google.com/d/optout. >>>>>>> >>>>>> >>>>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "sympy" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to [email protected]. >>>> To post to this group, send email to [email protected]. >>>> Visit this group at https://groups.google.com/group/sympy. >>>> To view this discussion on the web visit >>>> https://groups.google.com/d/msgid/sympy/f68853ca-2a1f-4ef1-a371-340602cbd63d%40googlegroups.com >>>> >>>> <https://groups.google.com/d/msgid/sympy/f68853ca-2a1f-4ef1-a371-340602cbd63d%40googlegroups.com?utm_medium=email&utm_source=footer> >>>> . >>>> >>>> For more options, visit https://groups.google.com/d/optout. >>>> >>> >>> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] <javascript:>. >> To post to this group, send email to [email protected] <javascript:> >> . >> Visit this group at https://groups.google.com/group/sympy. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sympy/16628e82-8a37-4ce4-8840-e6bcabcb7d20%40googlegroups.com >> >> <https://groups.google.com/d/msgid/sympy/16628e82-8a37-4ce4-8840-e6bcabcb7d20%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> >> For more options, visit https://groups.google.com/d/optout. >> > > -- You received this message because you are subscribed to the Google Groups "sympy" group. 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