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Appendices - Table of Contents Page Abstract 2 34...

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Table of Contents Page Abstract…………………………………………………………………… 2 Introduction…………………………………………………………………… …………………… 3 – 4 Analysis………………………………………………………………………… ……………………. 5 – 16 Position……………………………………………………………………… …………………… 5 – 8 Kinematic…………………………………………………………………… ………………….. 8 – 11 Coupler Pt. P ………………………………………………………………………………… 12 – 16 Results & Discussion (Case 2) ……………………………………………………………… 16 – 27 Conclusion…………………………………………………………………… …………………….. 28 Appendix A: Case 2 Data……………………………………………………………………. 29 – 37 Appendix B: Case 1 Data / Plots…………………………………………………………. 38 – 58
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Appendix C: Case 3 Data / Plots…………………………………………………………. 59 – 72 Appendix D: Method of Instant Centers……………………………………………… 60 – 76 Appendix E: Finite Difference Method………………………………………………… 77 – 89 Appendix F: Matlab Code…………………………………………………………………... 90- 107
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Abstract A complete kinematic analysis for the geared five-bar mechanism has been completed. The analysis included three separate cases for the gear ratios of the mechanism. A position synthesis was performed using the Newton-Raphson Method in which no singularities were determined for any of the three cases. The first- and second-order kinematic coefficients were solved and the angular velocity and acceleration was calculated. The values for the first-and-second order kinematic coefficients were checked using the method of instant centers as well as the finite difference method. The coupler point P was analyzed as well where a plot of the coupler curve was generated. The velocity and acceleration of the coupler point was also determined. It was determined that an initial value of the angle of link 3 between 90 and 100 degrees would produce a coupler curve that did not cross over itself. Introduction A kinematic analysis of linkages is an important tool in determining the correct size and position of the desired linkage. This allows for the design of the linkage to be optimized based on the desired parameters. The planar five-bar linkage shown in Figure 1 is mobility 2. That is, two different configurations are possible and two inputs must be considered.
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Figure : Planar Five-Bar Linkage When the two input links shown in Figure 1 are replaced by a set of gears then the outcome is a linkage with mobility 1.
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