By A. Gfrerrer (auth.), J. Lenarčič, M. M. Stanišić (eds.)
This ebook provides the latest study advances within the conception, layout, keep watch over and alertness of robot structures, that are meant for various reasons resembling manipulation, production, automation, surgical procedure, locomotion and biomechanics. the problems addressed are essentially kinematic in nature, together with synthesis, calibration, redundancy, strength regulate, dexterity, inverse and ahead kinematics, kinematic singularities, in addition to over-constrained structures. equipment used comprise line geometry, quaternion algebra, screw algebra, and linear algebra. those tools are utilized to either parallel and serial multi-degree-of-freedom platforms. the consequences may still curiosity researchers, academics and scholars, in fields of engineering and arithmetic on the topic of robotic concept, layout, regulate and alertness. All articles within the ebook have been stated on the 7th foreign symposium on Advances in robotic Kinematics that was once organised in June 2000 within the attractive old Mediterranean city of Piran in Slovenia. The previous symposia of the sequence came about in Ljubljana (1988), Linz (1990), Ferrara (1992), Ljubljana (1994), and Piran (1996), and Salzburg (1998).
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3) By the elimination of the output angles rpjll except for the last rpnll and regarding rpllI=rp21' rp211=rp31"'" rpn-I,Il=rpnI we get the transfer function of the multiple Hooke joint linkage in the form tan(rpnll) = cI>n tanrpll with cI>n = (COSAI ) p I ..... (COSA) p' J ••••• (COSAn)Pn . (4,5) The linkage is homokinematic if always is rpnll =rpll . That denotes tanrpnll = tanrpll and (6) Equation (6) is fulfilled by following conditions: Condition 1. The number of null and right plane Hooke joints is such that at least one is a null plane (power Pj= -1) and at least one is a right plane (power Pj = 1) Hooke joint.
Maybe the reason is they are 52 more difficult to program. An easy way of solving these problems was found with the dual method. The real parts and spherical mathematical models are coherent. So at first the tasks with angles and axis directions can be computed. Afterwards the dual parts lead mostly to a linear solution in the space. The geometry of spatial homokinematic linkages with four and that one with five Hooke joints are ready for publication. ezLO ZL Figure 7. Spatial homokinematic triple Hooke joint linkage track References Richtlinie VDI 2722 expected 2000 Gelenkwellen und Gelenkwellenstrange mit Kreuzgelenken Einbaubedingungen fUr Homokinematik, Beuth Verlag GmbH Berlin.
9, D-82065 Baierbrunn Germany Abstract. The structure of a Hooke or Cardan universal joint is a spherical four bar linkage. This linkage has in general ·a varying velocity transmission ratio. To get a homokinematic transmission, it is necessary to use at least two Hooke joints in a track of three shafts, the input shaft, the intermediate shaft and the output shaft. During a constant angular velocity of the input of the first Hooke joint the second Hooke joint has to compensate the variable angular velocity of the intermediate shaft driving the output shaft.