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

The CISM-IFToMM Symposia have performed a dynamic position within the improvement of the speculation and perform of robotics. The complaints of the 10th Symposia current a global view thus far of the cutting-edge, together with a special list of the consequences completed in important and jap Europe.

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

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2 a). A ring void is a ring shaped region of unreachable points surrounded by the workspace points. It can be detected, similarly to the case of the 3R algorithm developed in [7], by observing the central loop position in branch 4), also with respect to the branches 1) and 2) as previously noted. 2 a) and 4 a). 3 a). 3 and the great shape modification as a function of the geometrical parameters of the 4R open chain. 2 and 4. Three apple voids may occur in a general skew workspace cross-section of 4R manipulators since each envelope contour 1) and 3) may intersect Zl axis with one apple void.

B. B7 B7 detM =0 (18) 0 C, Cs c. C7 Cs C6 C7 0 By devoloping this determinant, we are led to an algebraic equation of order 40 ; but this equation can be factorized: the first of the three factors is (1+ y2)5 , the second , which summerizes the unwanted roots, is a polynom of order 10, and finally the third factor is a polynom of order 20, and this factor contains the solutions. Factorisation of the final polynom is only possible if the system parameters have been entered as integers. Otherwise one has to solve numerically the final equation of order 30 (the factor (1+ y2)5 can always be extracted) and then, by resubstitution, find out which roots solve the entire set of equations (8).

2. The target points for the winding arms when the number of the part performances defined for the winding operation J =6. 53 Discrete Calculation of Set Points The set point calculations for the movements of the winding arms are carried out using the nth degree polynomial. A profile function defined for a constant velocity is used to drive the rolls together. The functions are fitted between the target angles determined for tbe winding arms, see Fig. 2. ) In the formula (10), + I) Iljl = llA21lj llj2 = 21lj + 51lj + 3 llj3 = 41lj +81lj +3 llj4 = 41lAllj 2 2 +1) .

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