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]> 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]. > 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/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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