1. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 Generic model Figure Legend:

2. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 Shape function ϕ M00(τ) associated with contact point M 00 as defined in Fig. 6 Figure Legend:

3. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 Profile modification function Λ 00 (τ) associated with contact point M 00 as defined in Fig. 6 Figure Legend:

4. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 Optimum relief curve for LCR spur and helical gears Figure Legend:

5. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 Optimum relief curves for HCR gears Figure Legend:

6. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 Discretized contact lines—Base plane geometry at the initial time τ = 0 Figure Legend:

7. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 Modified profile relief Figure Legend:

8. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 Three-dimensional gear model (72 DOFs) Figure Legend:

9. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 RMS of quasi-static transmission error versus the normalized extent of modification (variation along the optimal relief curve as defined in Fig. 4). Gear A in Table 2. Figure Legend:

10. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 RMS of quasi-static transmission error versus the normalized extent of modification (variation along the optimal relief curve labeled (a) as defined in Fig. 5). Gear B in Table 2. Figure Legend:

11. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 RMS of quasi-static transmission error versus the normalized extent of modification (variation along the optimal relief curve labeled (c) as defined in Fig. 5). Gear B in Table 2. Figure Legend:

12. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 RMS of quasi-static transmission error versus the normalized extent of modification (variation along the optimal relief curve labeled (b) as defined in Fig. 5). Gear B in Table 2. Figure Legend:

13. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 RMS of quasi-static transmission error versus the normalized extent of modification (variation along the optimal relief curve as defined in Fig. 4). Gear C in Table 2. Figure Legend:

14. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 RMS of quasi-static transmission error versus the normalized extent of modification (variation along the optimal relief curve as defined in Fig. 4). Gear D in Table 2. Figure Legend:

15. Date of download: 9/18/2016 Copyright © ASME. All rights reserved. From: Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method J. Mech. Des. 2013;135(7):071009-071009-8. doi:10.1115/1.4024374 Optimum relief for (a) the nominal CD and (b) CD + 0.1 mm—Gear C in Table 2 Figure Legend: