**Apr 15, 2019 — Various shedding cams like linear, simple harmonic, parabolic, cycloidal etc. for designing plain and twill weave shave been considered. A **

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Submit Manuscript | http://medcraveonline.comIntroduction Cam-follower mechanism converts a rotary motion into a linear reciprocating motion. The input of cam rotary motion transforms into output as a follower motion consisting of rise, dwell and fall. The transition of dwell with rise and fall is an important aspect of cam design since the follower must go from a velocity and acceleration and fall of the follower have many possible motions such as linear, simple harmonic, parabolic, cycloidal etc. 1,2 The design of the cam desired displacement, velocity, acceleration and jerk. For excellent loom performance, the cams should be properly selected.3,4 The appropriate choice of cam is more enhanced in case of high speed looms which are required to maintain a high level of performance. Mali et al.5 design optimization of cam and follower mechanism. Patel 6 made a critical review on the design of cam and follower. Desai & Patel 7 made a computer aided kinematic and dynamic analysis of cam and follower. This study endeavors the computational plotting of different types with respect to their corresponding kinematics has also been discussed in this work. reciprocating or oscillating motion to another element known as follower. Conventionally, in a cam-follower system, the cam is follower are estimated once the cam displacement curve is designed. of which motion is communicated to the follower. In reality the stationary while the contact points between cam and follower revolves round the cam in the opposite sense of the actual cam rotation. With such an idea the locus of the successive touching points of tangents 8,9 The position of the follower depends on the centre-to-centre distance between cam and follower () and angle of the cam shaft rotation () as depicted in Figure 1. Therefore, if ,,,0 fxy describes the locus of the follower surfaces, the coordinates of the following two equations ,,,0 fxy (1) ,,, 0,fxy (2)Figure 1 The coordinates of cam and follower. Where ,f is the partial derivative with respect to and . For a cylindrical follower with radius as shown in Figure 1, the locus of its surface is given by: 2220xcosysinr (3)From which the partial derivative gives 2()(‘ )2()(‘ )0 xcoscossinysinsincos (4)Where’is the derivative of . By solving Equations (3) and (4), the x, y J Textile Eng Fashion Technol. 2019;5(2):126132.126©2019 Ghosh. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and build upon your work non-commercially. kinematic characteristicsVolume 5 Issue 2 – 2019 Correspondence: Received: | Abstract endeavored. Various shedding cams like linear, simple harmonic, parabolic, cycloidal kinematic characteristics for different types of cams suggests that the simple harmonic and cycloidal cams outperform parabolic and linear cams for high speed weaving. Keywords: shedding, weaveJournal of Textile Engineering & Fashion Technology Open Access

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127Citation: J Textile Eng Fashion Technol. 2019;5(2):126132. DOI: by: 22’rsincos xcos (5) 22’rcossin ysin (6)The two solutions of x and y correspond to the inner and outer During the rise and fall regions of the follower, is varied during the dwell position. The expression of in Equations (5) and (6) is substituted by: kS (7)Where S is the follower displacement with respect to the angle of cam shaft rotation. For a complete rotation of cam, is ranging from k tokh, where is the distance from the cam centre to the nearest position of the follower centre and h is the maximum lift of the follower. In this study the values of k, h and the crank shaft rpm are considered as 4cm, 5cm and 240rpm respectively. There are many possible motions such as linear, simple harmonic, parabolic, cycloidal etc. for the follower during its rise and fall. The equations of follower displacement ( ) with respect to the angle of cam shaft rotation for () various types of motion are given in the Table 1 where m, p and c are the constants. some basic weaves like plain and twill have been chosen with one third dwell period. Different types of basic motions such as linear, simple harmonic, single parabolic, double parabolic and cycloidal for the heald shaft during its lifting and lowering movement have been considered in this study. dwell at top position, lowering and dwell in bottom position. Table 2 & Table 3 depict the actual lifting and lowering equations of the follower displacement ( S) corresponding to different cams used in the shedding operation for plain and 3 1 twill weaves, respectively. The values of S during the dwell at top and bottom positions are remaining constants which are h and 0, respectively. For designing a S during the periods of lifting, dwell at top position, lowering and dwell at bottom position are replaced in Equation 7. Then the Equations 5 x and y over a range of from 0 to2 was used for the purpose of plotting. Figure 2 consists of four parts, namely the rise from 0 to 23 radian, the dwell from 23 to radian, the fall from to53 radian and another dwell from 53to2radian. d in 3 1 is consisting of the rise from 0 to 3radian, the dwell from 3to 2radian, the fall from2 to 56radian and ano ther dwell from 56 to2radian. Figure 2 camsThe velocity, acceleration and jerk equations can be obtained by differentiating the displacement equation with respect to time (t) by once, twice and thrice respectively. Therefore, the velocity, acceleration and jerk of the follower are give n bydSdt, 22 dSdtand33 dSdt, respectively. 10 Figures 4 and 5 depict the di splacement, velocity, acceleration and jerk plots of follower for different types of cams used for the plain weave shedding operation.The linear cam produces constant velocity but the main problem associated with this cam is that at the start and end of the dwell period, this cam cannot be suitable at high speed.The single parabolic cam produces linear velocity and constant (a) (b) (c) (d) (e)

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128Citation: J Textile Eng Fashion Technol. 2019;5(2):126132. DOI: acceleration during the lifting and lowering. During the end of the lifting motion and start of the lowering motion, the follower velocity the beginning and the end of the dwell period because the acceleration in high speed application. Figure 3 In case of double parabolic cam the velocity of follower during its rise and fall is represented by two straight lines having opposite slopes. The velocity of follower increases linearly, reaches maximum at the mid position and then start to fall linearly during the lifting and lowering movements but it becomes zero during the beginning and abruptly from positive to negative direction and vice versa during the this cam is not also desirable in high speed application.For a simple harmonic cam, velocity of the follower during its rise and fall represents by a sine curve while the acceleration of the same represents a cosine curve. The follower velocity remains zero at the start and end of the rise and fall which ensures a suitable linking with the dwell by means of smooth transition at the junction of zero nature of the jerk curve is in a direction opposite to the velocity curve. Thus it is quite suitable cam for high speed application. Figure 4 on the circumference of a circle which is rolling without slipping on a straight line. For a cycloidal cam, acceleration and jerk of the follower are represented by sine and cosine curves, respectively. Both the velocity and acceleration of follower are remaining zero at the start and end of the rise and fall. Therefore, a cycloidal cam ensures a perfect linking with the dwell caused by the smooth transition at the junctions of zero velocity as well as acceleration. Consequently, the speed application. (a) (b) (c) (d) (e) (a) (b) (c)

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129Citation: J Textile Eng Fashion Technol. 2019;5(2):126132. DOI: Figure 5 Types of motions Smc 2Spmc (1cos) Smp (sin) Smpp Comparison of various types of shedding cams The lifting motion of the follower corresponding to different types of shedding cams has been considered for the purpose of comparison. Figure 6 and Figure 7 depict the displacement, velocity, acceleration and jerk plots of the follower during its lifting motion.It is quite obvious from the Figure 6a that the follower displacement diagram of the linear cam is a straight line whereas in case of single parabolic cam it is parabolic and concave towards the displacement axis. In case of all but the single parabolic cam, the follower reaches the half of the displacement at the same time. The follower displacement of the simple harmonic, double parabolic and cycloidal cams shows a sigmoidal type of curve and the second half of the displacement curve during the lifting is a mirror image of that devotes maximum time during its initial and completion parts of the lifting movement, but it spends minimum time at the middle position of the lifting movement. On the contrary, the follower of the simple harmonic cam spends minimum time during the commencement and end of the lifting movement but at the middle position of the lifting it allows maximum time.Figure 6 The velocity plot of follower during lifting for various types of cams is shown in Figure 6b. The follower of linear cam has constant velocity. In case of single parabolic cam, the velocity of follower increases linearly from zero to maximum during the entire lifting motion. The velocity of the follower during the course of lifting motion for simple harmonic, double parabolic and cycloidal cams commences from zero, reaches to peak at the centre position of the lift and again becomes zero at the end. In case of double parabolic to simple harmonic cam, the follower velocity of the cycloidal cam during its lifting motion starts in a slower and smoother manner, at the middle of the lift it becomes faster and at the end position it reduces more gradually. The peak velocities of double parabolic and cycloidal cams are higher than the simple harmonic cam. Figure 7a depicts the acceleration plot of follower generated and end of the lift, but rest of the time during the lift it remains zero. The follower acceleration remains at a constant value for single parabolic cam. The follower acceleration of double parabolic cam is also constant but changes its direction from positive to negative (a) (b) (a) (b)

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130Citation: J Textile Eng Fashion Technol. 2019;5(2):126132. DOI: at the mid position of lifting. In case of simple harmonic cam, the the start and end of the rise; and it becomes zero at the mid of the rise. On the other hand, the follower acceleration of cycloidal cam the follower acceleration for double parabolic, simple harmonic and but opposite in direction. Cam type 3 1 Cam type 20332hS31cos 22hS 2294hS22229, 0 32962 , 332hShh h 3sin3 2hS 533522 hhS 31cos 222 hS 2291525 244hhh S 22229974 , 2329152545 , 233 2hhh Shhh 3sin3 2hSh 03 3hS1cos3 2hS 229hS222218, 0 61812 , 63hShhh 6sin6 2hS 526 352hhS 1cos3 22hS 2291525 4hhh S 222218187 4, 226 18302545 , 266 hhh Shhh 6sin6 222 hSh The jerk plot of the follower during its lifting for various cam noise are expected for the simple harmonic and cycloidal cams. The follower jerk of simple harmonic motion is zero at the start and end of

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131Citation: J Textile Eng Fashion Technol. 2019;5(2):126132. DOI: Overall, simple harmonic cam generates less jerkiness than that of cycloidal cam.Figure 7 used in plain weave design. It is clear from Figure 8 that each cam two dwell positions is concerned, the distance from the cam centre to its surface changes more gradually for the cycloidal cam followed by provide bumpy connection between the dwell and changeover parts.Figure 8 kinematics of the follower motion reveals that linear and parabolic the start as well as a perfect linking with the dwell and the changeover positions. The simple harmonic and cycloidal cams are suitable for high speed weaving. None. References 1. Bevan T. The theory of machines. 3rd ed. New Delhi: Pearson India; 2010.2. Illinois: Waveland Press Inc; 2002. 3. Institute; 1976.4. 5. and follower mechanism of an internal combustion engine for improving Modern Mechanical Engineering. 2012;2(3):114Œ 119. 6. Patel NS. Modelling, design and analysis of cam and follower-a review. International Journal of Engineering Studies and Technical Approach . 2015;1(2):1Œ7.7. Engineering; 2010;2:117Œ127. (a) (b)

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