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By A. Morecki, G. Bianchi, K. Jaworek

The CISM-IFToMM Symposia have performed a dynamic function within the improvement of the idea and perform of robotics. The court cases of the 10th Symposia current a global view so far of the cutting-edge, together with a distinct checklist of the implications completed in important and japanese Europe.

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By A. Morecki, G. Bianchi, K. Jaworek

The CISM-IFToMM Symposia have performed a dynamic function within the improvement of the idea and perform of robotics. The court cases of the 10th Symposia current a global view so far of the cutting-edge, together with a distinct checklist of the implications completed in important and japanese Europe.

Show description

Read or Download Theory and Practice of Robots and Manipulators: Proceedings of RoManSy 10: The Tenth CISM-IFToMM Symposium PDF

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Additional resources for Theory and Practice of Robots and Manipulators: Proceedings of RoManSy 10: The Tenth CISM-IFToMM Symposium

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And in both other cases a polynom of degree 18. POSITION ANALYSIS First case. The equation x y = 1 is equivalent to: 1{12 = H - I{II • it is the case in which the rhombic polygon is open. With y = 1/ x we obtain from (8) three equations in the in the variables X. Y and x for which we can write: GI = Gl1 X2 +G I2 X+G I3 = O. 1 = O. (12) where the coefficients G" are quadratic polynoms in x as well in Y. As the simultaneous existence of the three homogeneous equations (12) demands the vanishing of coefficient determinant we get a first equation in X and Y from (13) By developing (13) and splitting up a factor (I+X2)(I+y2) we obtain an algebraic equation of order four in X and in Y for which we write 26 K.

X. y ) = 0 • y) =0 y) =0 (8) This specific structure let expect that a solution could be found by eliminating first the two unknowns x and y. It is possible to derive from the equations 25 Position Analysis of the Rhombic Assur Group (8) two polynomes of degree 12 and one of degree 14 in both of the variables X and Y. Elimination of one of these two variables by Sylvester's Method [7] leads to a 19x19 matrix. whose determinant equated to zero would yield an algebraic equation of order 238. With the present facitilies it is impossible to estabish this equation which.

If the remaining three input pOints are fixed. 3). 3 and all pOints of the link to which K3 belongs too. describe a "higher coupler curve". 4 for which all the 56 positions would turn out to be real. we could conclude that these coupler curves are fullcircular algebraic curves of order 56. 4 than 56. I. Ten of the positions of the rhombic Assur group are real. 4 shows these positions. 9 + lll. 893 + 101. 101. 59 + 41. 35 + 41. 401 + 1 51. 94 i 51. 94 i 1. 757 i 1. 72 67. 67. 24 11. 52 11. 8 41.

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