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Unformatted text preview: Results and Discussion This section presents the results obtained through the analysis described above for the geared fivebar linkage. Three different designs of the geared fivebar linkage have been considered. For case one, the radius of gear 2 is 2 inches and the radius of gear 3 is 3 inches. For case two, the radius of gear 2 is 3 inches and the radius of gear 3 is 3 inches. For case three, the radius of gear 2 is 4 inches and the radius of gear 3 is 2 inches. As stated above, the angular velocity of input link 2 is a constant 10 rad/sec. This section will present the results for case two, when the gear ratio is onetoone. The results for case one is shown in Appendix B and the results for case three can be found in Appendix C. For case two, the input link began at zero degrees and rotated counterclockwise 360 degrees in 5 degree increments. Using the NewtonRaphson method described the position variables for links 3, 4, and 5 were determined. The plot of the position variables of links 4 and 5 is shown in Figure 4a while the plot of the position variables for link 3 is shown in Figure 4b. The numerical values for the position variables of links 3, 4, and 5 are shown in Table 3 found in Appendix A. Figure 4a: Position Variables Links 4 and 5 against Input position Figure 4b: Position Variable Link 3 against Input Position It can be seen in Figure 4a that both links make a complete turn. This conclusion is made because the plot shows that both links return to their initial position. Figure 4a not only gives the position analysis for links 4 and 5 but also confirms that the conditions of the input link are acceptable for this analysis. Equation 9 shows that the singular configurations occur when the angle of link 4 differs the angle of link 5 by 180 degrees or when the two angles are equal. It is clear from Figure 4a that neither of these conditions is satisfied and thus a singular position does not when the radius of gear 2 is 3 inches and the radius of gear 3 is 3 inches. To verify that a singular position does not occur for case two, a plot of the value of the determinate versus the input link is shown in Figure 2. It is clear from Figure 5 that the determinate value at no point obtains a value of zero. It was found that no singular position occurred for any of the three different gear ratios. The closest any of the different gear ratios had to becoming singular was for Case 1 at an input position of approximately 390 degrees. Figure 5: Determinate versus Input Position Next, the firstorder kinematic coefficients were found using equations (16a) and (16b). The numerical values found for the firstorder kinematic coefficients for case two can be found in Table 3 located in Appendix A. Figure 6 below plots the firstorder kinematic coefficients versus the input position. Figure 6: FirstOrder Kinematic Coefficients Versus Input Position The secondorder kinematic coefficients were found using equations (19a) and (19b). The numerical values obtained are given in Table 3 located in Appendix A. numerical values obtained are given in Table 3 located in Appendix A....
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 Fall '08
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