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) 5. 3. THE MECHANISM STRUCTURE The structural diagram of the mechanism is given in Fig. 2. The mobility degree is: M=3n-2C 5 -C 4 =3.4-2.5=2, the mechanism having two conductive elements and a BCC dyad of RTR type. 18
Fig. 1 Fig. 2 4. THE MECHANISM KINEMATICS The correlation between angles and is obtained (Fig. 3), through the relations: Fig. 3 19
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 120...0. 20
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 120...0. ). Fig. 6 Fig. 7 21
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. 1500. 1000. 500. S S2 S3 0.0-500.0 0.0 100. 200. 300. 400. Fig. 10 22
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. 800. 600. 400. 200. 0.0 X B Y B X F Y F -200.0-400.0 0.0 100. 200. 300. 400. Fig. 11 The same observation applies to the E and C coordinates in Fig. 12. 1000. 800. 600. 400. X C Y C X E Y E 200. 0.0 0.0 100. 200. 300. 400. Fig. 12 23
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. 1000. 750. 500. 250. X E Y E X F Y F 0.0-250.0 0.0 100. 200. 300. 400. 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 80 427.0933 354.5575 427.0948 345.4423 81 421.9293 353.6933 421.9307 346.3065 82 416.7509 352.9194 416.7523 347.0804 83 411.5598 352.236 411.5611 347.7638 84 406.3575 351.6433 406.3589 348.3565 85 401.1457 351.1415 401.1471 348.8584 86 395.926 350.7307 395.9273 349.2692 87 390.6999 350.4111 390.7012 349.5889 88 385.4688 350.1827 385.4702 349.8172 89 380.2347 350.0457 380.2361 349.9543 90 374.999 350 375.0003 350 91 369.7633 350.0457 369.7647 349.9544 92 364.5291 350.1828 364.5305 349.8173 93 359.2982 350.4112 359.2996 349.5889 94 354.072 350.7308 354.0734 349.2692 95 348.8523 351.1417 348.8537 348.8584
96 343.6405 351.6436 343.6419 348.3566 97 338.4383 352.2363 338.4396 347.7639 98 333.2472 352.9197 333.2485 347.0805 99 328.0687 353.6937 328.0701 346.3066 100 322.9046 354.5578 322.9059 345.4424 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. 450. 425. 400. 375. 350. X E Y E X F Y F 325. 300. 80. 85. 90. 95. 100. Fig. 14 355. 350. 345. X E Y E X F Y F 340. 80. 85. 90. 95. 100. Fig. 15 25
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, 2009. 3]. 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. 372-380. [4]. Kojevnikov, S. N., Esipenko, Ia. I., Raskin, Ia. M., Mehanizmî. Sparvocinâe posobie. Izd. Maşinostroenie, Moskva, 1976. [5] Popescu, I., Luca, L., Cherciu, M., Structura şi cinematica mecanismelor. Aplicaţii. Editura Sitech, Craiova, 2013. 26