KINEMATICS OF A SCISSORS MECHANISM
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1 KINEMATICS OF A SCISSORS MECHANISM Prof. PhD. Liliana LUCA, Constantin Brancusi University of Targu-Jiu, lylyanaluca@yahoo.com Prof. PhD. Iulian POPESCU, University of Craiova, rodicaipopescu@yahoo.com Abstrac:. We study the kinematics of a scissors mechanism composed of two conductive elements with related movements and a RTR type dyad. They are written the relations based on contours method and they are given the results in tables and diagrams. Keywords: mechanisms for scissors, kinematic analysis, two conductive elements. 1. INTRODUCTION The mechanisms from the scissors of debitting metals have been studied over time by various methods. Many of them were built empirically, on summary calculations. Computers and new analytical analysis methods allow more detailed studies, which led to improving the performance of these mechanisms. In the literature, studies continue to show this theme. Thus, in [1] it is studied the kinematics of a scissors mechanism with a triad, which is intended for cutting of steel products. They are given the analytical relations based on contours method and numerous resulted diagrams. In a doctoral thesis [2] they are studied in detail the mechanisms that ensure shear cutting branches of trees in order to clean them. They are studied different variants of mechanisms, by modeling them. A detailed dynamic study on a shear mechanism is given in [3]. The mechanism consists of two dyads.they are calculated the positions, velocities, accelerations and reactions of couplings. 2. INITIAL DATA We left from the kinematic scheme of a mechanism given in [4] and shown in Fig. 1. Items 1 and 4 are both leading, with movements linked by a gear, cog belts, chain Galle chain or other system. In E and F points are the tips of two knives that run the shear, point F being on the element 2 which is having a flat movement and point E belongs to element 3, which also has a flat movement. The symmetry properties of the mechanism allow for a position of the mechanism the knives to cut the blank (sheet) THE MECHANISM STRUCTURE The structural diagram of the mechanism is given in Fig. 2. The mobility degree is: M=3n-2C 5 -C 4 = =2, the mechanism having two conductive elements and a BCC dyad of RTR type. 18
2 Fig. 1 Fig THE MECHANISM KINEMATICS The correlation between angles and is obtained (Fig. 3), through the relations: Fig. 3 19
3 φ - α= 90 (1) Ψ+ α= 270 (2) Ψ+ φ - 90=270 (3) Ψ=360- φ (4) For the kinematic analyze, they are written the relations: x B =x A +ABcosφ (5) y B =y A +Absinφ (6) x C =x D +CDcosψ (7) Y C =Y D +CDsinψ (8) S=y C -y B (9) S 2 =y B + BF (10) S 3 =y C -CE (11) x F =x B -a (12) y F =y B +BF (13) x E =x C -a (14) y E =y C -CE (15) We have adopted the following initial values: XA = 400: XD = 400: YD = 700: BF = 50: CE = BF: AB = 300 CD = AB: A = BF / 2. 5.THE OBTAINED RESULTS In the FIG. 4 it is shown the mechanism for = 120 degrees. The image is similar to that of FIG. 1, so the program is done correctly. The two points of the figure are the E and F points, that is the tips of the knives for this position. The successive positions of the mechanism are shown in Fig. 5 for
4 Fig. 4 Fig. 5 It is noted that while element 1 rotates clockwise, item 4 rotates counterclockwise. The figure also shows the trajectories of E and F points, thus the trajectories of knives peaks. At a full rotation they result the successive positions of Fig. 6. The trajectories of tops knives are circles and race S, meaning the distance between C and B, is variable (fig. 7 for ). Fig. 6 Fig. 7 21
5 The complete trajectories of E and F points are shown in Fig. 8, and they are circles with centers that are different of A and D (Fig. 9), as E and F are located close to the C and B but offset to their left. In the figure also appear and C and B circles. Tangent circles of FIG. 9 are described by E and F. Fig. 8 Fig. 9 The variations of S, S2 and S3 races to the position of the mechanism are shown in Fig. 11. It is observed that the minimum S, S2 and S3 races are equal to 90 degrees S S2 S Fig
6 Referring to FIG. 11, it is shown that diagrams for coordinates variation of the F and B points are very close, the shifts being determined by the fact that E and F are also staggered relative to the BC element X B Y B X F Y F Fig. 11 The same observation applies to the E and C coordinates in Fig X C Y C X E Y E Fig
7 For the drawer, it is interesting the contact area between the blade tips. To this, they were plotted in FIG. 13 the coordinates of E and F points, observing that for of about 90 degrees, YE and YF curves are tangent, meaning the E and F points coincide, this is the shearing time X E Y E X F Y F Fig. 13 In Table 1 they are also given the numerical results for this area of the operating cycle of the mechanism. Table 1 24 Fi XE YE XF YF
8 It appears that indeed, at = 90, YE = YF. It has been enlarged the diagram of FIG. 13 in the area of interest, finding fig. 14 and 15, where it is clear the tangency of the two circles and the equality of the two ordinates X E Y E X F Y F Fig X E Y E X F Y F Fig
9 6. CONCLUSIONS - The studied mechanism satisfies the condition of blank shear. - Although blades are having a flat movement, they have trajectories that become tangent when shearing. - From constructive point of view, these knives can be even on BC element, without the offset. - The mechanism is cleverly designed. REFERENCES [1]. Berghian, A. B., Vasiu, Th., Kinetics study on laboratory model of the mechanisms of parallel gang sheoars type assigned for cutting metallurgical products. Journal of Engineering annals of Faculty of Engineering Hunedoara, tome V, 2007, fasc. 3. [2]. Maglioni, C.,Analysis of reciprocating single blade cutter bars. Tezi di Dottorato. Universita di Bologna, ]. Tyagi, R. K., Verma, M., Borah, S., Dynamic analysis of a shaper machine cutting tool and crank pin. Journal of Enviromental Science, Computer Science and Engineering & Technology, sept.- nov. 2012, vol. 1 no.3, pp [4]. Kojevnikov, S. N., Esipenko, Ia. I., Raskin, Ia. M., Mehanizmî. Sparvocinâe posobie. Izd. Maşinostroenie, Moskva, [5] Popescu, I., Luca, L., Cherciu, M., Structura şi cinematica mecanismelor. Aplicaţii. Editura Sitech, Craiova,
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STRUCTURE AND KINEMATICS OF A MECHANISM WITH STOPS Prof.PhD. Liliana LUCA, University Constantin Brancusi of Targu-Jiu, lylyanaluca@yahoo.com Prof.PhD. Iulian POPESCU, University of Craiova, rodicaipopescu@yahoo.com
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