本研究提出一個創新的爬梯機構，相較於現有爬梯機器多以滾輪型、履帶型、多足獨立控制型或多足連桿式相依控制型機構進行爬梯，有機身起伏大造成的不平穩、摩擦力不足造成的滑動現象、控制複雜等問題，本研究之爬梯機構可避免這些缺點。本研究以單自由度之純滾動機構為設計理念，應用旋輪線理論找出對數螺線形輪廓做為觸地桿的形狀設計，使機身進行直線平移，並使用非圓形齒輪於相位的規劃，達成不同相位分工合作及機身定速度直線平移的目的。該機構僅需單一動力輸入源即可驅動運行，機身穩定且無明顯晃動現象。本研究使用SolidWorks模擬軟體對機器人進行動力學分析，將理論結果、模擬結果進行比較驗證。本研究之爬梯機構於移動過程，機身的運動為定速度直線平移運動，適合用在需要高穩定性之場合。

This study presents an innovative stair-climbing mechanism. Comparing to the existing stair-climbing mechanisms such as roller type, track type, multi-leg independent control type or multi-leg link type dependent control mechanism, stair-climbing mechanism developed in this study can avoid the shortcomings, such as the sliding phenomenon caused by insufficient friction and the complicated controling problem. In this study, the design concept of pure rolling mechanism with single degree of freedom is applied. The theory of roulettes is used to find the logarithmic spiral contour as the shape of the leg link, so that the body can be linearly translated and the non-circular gears are used in the phase planning to achieve the purpose of different phase cooperation that divide the work and the linear translation of the body's constant speed. The design only needs a single power input source to drive the mechanism. The body is stable during operation and there is no obvious osculating phenomenon. In this study, the simulation software SolidWorks was used to analyze the dynamics of the robot, and the theoretical results and simulation results were compared. In the moving process, the body of the stair-climbing mechanism is a linear translational motion with a constant speed.

[1] Stair bear climbing various stairs, from
https://www.youtube.com/watch?time_continue=168&v=JD1Su34tI_Q.
[2] Senior design project: stair climbing robot, from
https://www.youtube.com/watch?v=46qEgN3eqkA.
[3] Stair climbing robot (triple bended crosswheels), from
https://www.youtube.com/watch?v=hBFf0pZjY94&t=16s.
[4] V. Krys, Z. Bobovský, T. Kot, and J. Marek, “Synthesis of action variable for motor controllers of a mobile system with special wheels for movement on stairs,” perspectives in science, vol. 7, pp. 329-332, 2016.
[5] Rocker bogie mechanism concept, stair climbing robot,animation, using solidworks motion study, from https://www.youtube.com/watch?v=xlp3x-dAYjM.
[6] Bartholomew, from https://team1640.com/wiki/index.php?title=Bartholomew.
[7] M. Moghaddam, and M. Dalvand, “Stair climbing mechanism for mobile robots (Msrox),” Tehran International Congress on manufacturing engineering, 2005.
[8] M2 stair climbing hand truck, from http://www.handtrucksrus.com/product-details.aspx?id=1480&cx=bp.
[9] M. Khot, A. Gumaste, and V. Jagdale, “design and development of step climbing wheel chair,” Mechanical Engineering Department, Walchand College of Engineering Sangli,India, vol. 2, 2016.
[10] Stair climbing robot, from https://www.youtube.com/watch?v=OdJpDXZEkU0.
[11] Stair climbing mobile robot - ARTI: Rugged commercial platform, from https://www.youtube.com/watch?v=sohpgx6j_lk.
[12] Scalevo - The stairclimbing wheelchair - ETH Zurich, from https://www.youtube.com/watch?time_continue=121&v=3lb_8nmy90c.
[13] RHex, from https://www.bostondynamics.com/rhex.
[14] Spot, from https://www.bostondynamics.com/spot.
[15] Robot kicking soccer ball, from https://www.alamy.com/stock-photo/robot-kicking-soccer-ball.html.
[16] Linkage stair climber, from https://www.youtube.com/watch?v=krd6gfkTNwM.
[17] 林孟弦, “模仿人類爬梯步態之創新八連桿足型機構最佳設計與多足爬梯機器人設計之研究,” 成功大學機械工程學系學位論文, pp. 1-134, 2016.
[18] 黃盈嘉, “創新八連桿足型爬梯機構設計與軌跡最佳化之研究,” 成功大學機械工程學系學位論文, pp. 1-143, 2017.
[19] R. C. Yates, “curves and their properties,” 1974.
[20] E. H. Lockwood, A book of curves: Cambridge University Press, 1967.
[21] Roulette (curve) , from https://en.wikipedia.org/wiki/Roulette_(curve).
[22] Cycloid, from https://en.wikipedia.org/wiki/Cycloid.
[23] Involute, from https://en.wikipedia.org/wiki/Involute.
[24] M. P. Do Carmo, Differential geometry of curves and surfaces: revised and updated second edition: Courier Dover Publications, 2016.
[25] V. Volterra, Theory of functionals and of integral and integro-differential equations: Courier Corporation, 2005.
[26] J. Farrell, and M. Barth, The global positioning system and inertial navigation: Mcgraw-hill New York, 1999.
[27] D. Baleanu, S. Z. Nazemi, and S. Rezapour, “Existence and uniqueness of solutions for multi-term nonlinear fractional integro-differential equations,” advances in difference equations, vol. 2013, no. 1, pp. 368, 2013.
[28] T. A. Cook, The curves of life: being an account of spiral formations and their application to growth in nature, to science, and to art: with special reference to the manuscripts of Leonardo da Vinci: Courier Corporation, 1979.
[29] C. Berge, Topological spaces: including a treatment of multi-valued functions, vector spaces, and convexity: Courier Corporation, 1963.
[30] Logarithmic spiral, from https://en.wikipedia.org/wiki/Logarithmic_spiral.
[31] C. Moss, and C. Plumpton, "Integration by substitution," Integration, pp. 7-12: Springer, 1983.
[32] J. A. Sethian, Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science: Cambridge university press, 1999.
[33] Level set, from https://en.wikipedia.org/wiki/Level_set.
[34] S. Izumiya, “Singular solutions of first‐order differential equations,” Bulletin of the London Mathematical Society, vol. 26, no. 1, pp. 69-74, 1994.
[35] N. K. Ibragimov, and N. K. Ibragimov, elementary Lie group analysis and ordinary differential equations: Wiley New York, 1999.
[36] H. Whitney, “Regular families of curves,” Annals of Mathematics, pp. 244-270, 1933.
[37] D. Manocha, and J. F. Canny, "Detecting cusps and inflection points in curves," curves and surfaces, pp. 315-319: Elsevier, 1991.
[38] Singular solution, from https://en.wikipedia.org/wiki/Singular_solution.
[39] K. H. Rosen, Discrete mathematics and its applications: New York: McGraw-Hill, 2011.
[40] E. Kreyszig, Introductory functional analysis with applications: Wiley New York, 1978.
[41] I. M. Gelfand, and R. A. Silverman, Calculus of variations: Courier Corporation, 2000.
[42] L. D. Elsgolc, Calculus of variations: Courier Corporation, 2012.
[43] P. R. Halmos, Naive set theory: Courier Dover Publications, 2017.
[44] K. Knopp, Theory of functions: Courier Corporation, 1996.
[45] A. A. Fraenkel, Y. Bar-Hillel, and A. Levy, Foundations of set theory: Elsevier, 1973.
[46] C. D. Meyer, Matrix analysis and applied linear algebra: Siam, 2000.
[47] L. V. Ahlfors, “Complex analysis: an introduction to the theory of analytic functions of one complex variable,” New York, London, p. 177, 1953.
[48] J. Sondow, “Analytic continuation of Riemann’s zeta function and values at negative integers via Euler’s transformation of series,” Proceedings of the American Mathematical Society, vol. 120, no. 2, pp. 421-424, 1994.
[49] O. Christensen, An introduction to frames and Riesz bases: Springer, 2003.
[50] B. Laczik, “Design and manufacturing of non-circular gears by given transfer function,” TUB Budapest, Hungary, 2007.
[51] W. Smith, “The math of noncircular gearing,” Gear Technology, July/August, 2000.
[52] I. Zarębski, and T. Sałaciński, “Designing of non-circular gears,” Archive of Mechanical Engineering, vol. 55, no. 3, pp. 275-292, 2008.
[53] J.-Y. Liu, and Y.-C. Chen, "A design for the pitch curve of noncircular gears with function generation," Proceedings of the International MultiConference of Engineers and Computer Scientists , vol. 2,2008.
[54] I. Vaisman, Cohomology and differential forms: Courier Dover Publications, 2016.
[55] H. Kautz, and B. Selman, "Pushing the envelope: planning, propositional logic, and stochastic search." pp. 1194-1201.
[56] H. S. Wilf, generatingfunctionology: AK Peters/CRC Press, 2005.
[57] G. F. Simmons, and G. F. Simmons, Calculus with analytic geometry: McGraw-Hill New York, 1996.
[58] Monotonic function, from https://en.wikipedia.org/wiki/Monotonic_function.
[59] Monotonic functions, from https://www.math24.net/monotonic-functions/.
[60] Gears, from http://www.thefullwiki.org/Gears.
[61] J. W. Harris, and H. Stöcker, Handbook of mathematics and computational science: Springer Science & Business Media, 1998.
[62] 顏鴻森, 吳隆庸, 機構學, 東華書局, 2006.
[63] C^k Function, from http://mathworld.wolfram.com/C-kFunction.html.
[64] G. Birkhoff, Lattice theory, American Mathematical Soc., 1940.
[65] S. K. Godunov, “A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics,” Matematicheskii Sbornik, vol. 89, no. 3, pp. 271-306, 1959.