高爾夫球市場伴隨龐大高爾夫球運動器材市場與商機，尤其以球具功能重要。高爾夫球器材廠商持續導入先進製程與設計，持續球具的研發、開發與設計以幫助高爾夫參與者達最佳表現。研究目的針對使用不同高爾夫球桿面對於推桿表現之影響，針對其推桿動作與球滾動之運動學參數。受試對象為22名受過高爾夫球運動專項訓練的體育系男性，並進行兩公尺與四公尺距離測試。本研究使用超聲波儀器 (Puttlab 6, Science & Motion Sports, GmbH, Flörsheim, Germany, 70Hz *3)進行推桿運動數據蒐集。球滾動參數使用高速攝影機 (BlackFly, FLIR Systems, Virginia, USA, 120Hz)，以橫狀面座標校正後進行捕捉與分析。本研究針對市場推桿表面加工參數之推桿進行進球率、推桿與球滾動運動學蒐集並進行單因子變異數分析(α = .05)，如達差異則利用LSD法進行事後比較。接者針對水平出球角度、球初速度與球滾動距離進行多元迴歸分析。結果發現桿面有加工的進球率不管是兩公尺與四公尺都較高。加工深度會影響滑度比例與滾動比例，但不一定會降地球滾動距離。多元迴歸結果顯示推桿桿面為影響出球角度最主要因子。桿頭速度為影響出球速度最主要因素，上擊球角度未增加出球速度。出球速度、速度比例與滾動比例為影響球滾動距離最主要因素。研究結果對於未來推桿設計上很有幫助並且可應用在推桿教學應用。未來研究可針對不同果嶺速度、距離與果嶺坡度進行資料蒐集，並加入更多運動生物力學參數分析。

The golf market is accompanied by vast golf equipment and business opportunities, especially the advancement in the golf equipment performance and function. Golf equipment manufacturers consistently introduce advanced manufacturing processes, R&D, designs, and continue to develop and help golf participants achieve their best performance. There have been very few researches on human using different face milling putters. Most research used mechanical or simulation as the primary analysis method and did not collect the kinematic parameters of putter and ball rolling. Twenty-two healthy males were conducted as subjects with experiment distances from two and four-meters distances. The study used the ultrasonic instrument (Puttlab 6, Science&Motion Sports, GmbH, Flörsheim, Germany, 70Hz *3) to collect putting kinematic data. The ball rolling parameters are captured and analyzed using a high-speed camera (BlackFly, FLIR Systems, Virginia, USA, 120Hz) positioned on the transverse plane above the intended line of putt. The face geometries that were tested were the mainstream face milling parameters. ANOVA variance analysis (α = .05) was performed to analyze between face geometries and putter-ball kinematic data, and the LSD method was used for post-hoc analysis. Multiple regression analysis was implemented to determine critical predictors for the horizontal angle of the ball, the initial ball velocity, and the ball rolling distance. The study concludes that putter face milling can enhance putting performance. Deep milling may increase roll ratio but does not loss of ball distance. The putter face angle is the main predictor for horizontal launch angle, and roll ratio is predictive for horizontal launch angle from four meters. Putter velocity is the main predictor of ball velocity. A positive rise angle does not enhance ball velocity. Ball velocity and roll ratio are two main predictors to roll distance. Findings will be beneficial for future putter equipment design and putter coaching. Future studies can add biomechanical data along with different green speed, distance, and slope.

Aldrich, D. (2004). Surface engineering and golf. Surface Engineering, 20(1), 1-3.

Alessandrini, S.M. (1995). A motivational example for the numerical solution of two-point boundary-value problems. SIAM review, 37(3), 423-427.

Alexander, D.L., Kern, W. (2005). Drive for show putt for dough? An analysis of the earnings of PGA tour golfers. Journal of Sports Economics, 46(6), 46-60.

Arakawa, K., Mada, T., Komatsu, H., Shimizu, T., Satou, M., Takehara, K., & Etoh, G. (2007). Dynamic contact behavior of a golf ball during oblique impact: Effect of friction between the ball and target. Experimental mechanics, 47(2), 277-282.

Bowerman, B. L., & O'connell, R. T. (1990). Linear statistical models: An applied approach. Brooks/Cole.

Brouillette, M. (2010). Putter features that influence the rolling motion of a golf ball. Procedia Engineering, 2 2(2), 3223-3229.

Brouillette, M., & Valade, G. (2008). The effect of putter face grooves on the incipient rolling motion of a golf ball. In Science and golf V. Proceedings of the world scientific congress of golf. Ironwood Lithographers, USA (pp. 363-368).

Burnham, P., Wilkinson, M., & Goodall, S. (2013). The 2010 Regulations on Golf Club Groove Design: Impact on Ball Flight Characteristics During a Controlled Shot.

Butdee, S., & Punpojmat, S. (2007). Innovative design for an adjustable golf putter. The Journal of Industrial Engineering, 24(26), 867-871.

Carnahan, J. V. (2002). Experimental study of effects of distance, slope and break on putting performance for active golfers. In Science and Golf IV: Proceedings of the World Scientific Congress on Golf, (pp. 113-126).

Chou P. C, & Liang, D, Yang, L, & Gobush W. (1994). Contact forces, coefficient of restitution, and spin rate of golf ball impact. In 'Science and Golf II: Proceedings of the Second World Scientific Congress of Golf Ed. By A. J. Cochran & M. Farrally.E & FN Spon. London, Pg 296-301.

Cleaver, R. n.d. Club Masters. The scoring club. Available at: www.clubmasters.co.uk/articles/article4.html.

Cochran, A., Stobbs, J. (1986). Search for the perfect swing: The proven scientific approach to fundamentally improve your game. Chicago, Triumph.

Cochran, A. J., & Farrally, M. (Eds.). (2002). Science and Golf II: Proceedings of the world scientific congress of golf. Taylor & Francis.

Coello, Y., Delay, D., Nougier, V., & Orliaguet, J. P. (2000). Temporal control of impact movement; the time from departure control hypothesis in golf putting. International Journal of Sport Psychology, 31(1), 22-46.

Cornish, J., Otto, S., & Strangwood, M. (2008). Modelling the Oblique Impact of Golf Balls (P128). In The Engineering of Sport 7 (pp. 669-675). Springer Paris.Chou, A.C.P. (2004). Engineering methodology in golf studies. in “Biomedical engineering principles in sports”. In: Hung, G.K., Pallis, J.M. (Ed.). Springer.

Cross, R. (2006). Golf physics of golf. Sydney University.

Daish, C.B. (1972). The physics of ball games. English Universities Press.

Delay, D., Nougier, V., Orliaguet, J. P., & Coello, Y. (1997). Movement Control in Golf Putting, Human Movement Science, 16(5), 597-619.

DeGunther, R. (1996). The art and science of putting. Chicago, IL: Master Press.

Delphinus, E. M., & Sayers, M. G. (2012). Putting proficiency: contributions of the pelvis and trunk. Sports Biomechanics, 11(2), 212-222.

Drane, P., Duffy, M., Fournier, J., Sherwood, J., & Breed, M. (2014). The Behaivor of Golf Ball Putting on Artificial Turf, Procedia Engineering, 72(2014), 598-604.

Fairweather. M. M. (2002). A critical examination of motor control and issues in putting. In: Thain E, editor. Science and Golf VI. Proceedings of the 2002 World Scientific Congress of Golf: St Andrews London: E & FN Spon, 100-112.

Faulkner, E. M., Otto, S. R, & Strangwood, M. (2002). Characterisation and modelling of the vibration frequency of oversized golf drivers, The Engineering of Sport, 4, 255-261.

Gobush, W. (1995). Spin and the inner workings of a golf ball. Golf--The Scientific Way, Aston Publishing Group, Hemel Hempstead, UK, 141, 145.

Gwyn, R.G., Ormund, F., & Patch, C.E. (1996). Comparing putters with a conventional blade and a cylindrically shaped club-head. Perceptual and motor skills 82, 31-34.

Halliday, D., Resnick, R., & Walker, J. (2001). Fundamentals of Physics. Wiley & Sons Inc. New York.

Hasegawa, Y., Koyama, S., & Inomata, K. (2013). Perceived distance during golf putting. Human movement science, 32(6), 1226-1238.

Hurrion, P.D., Hurrion, R. D. (2002). An investigation into the effect of the roll of a golf ball using the C-groove putter. in “Science and golf IV: Proceedings from the world scientific congress of golf”. 4th, Thain, E, London, Routledge, 2002.

Hurrion, P. D., & MacKay, J. (2012). A rolling brief. Golf International, 111, 107-111.

Iwatsubo, T., Kawamura, S., Miyamoto, K., & Yamaguchi, T. (2000). Numerical analysis of golf club head and ball at various impact points. Sports Engineering, 3(4), 195-204

Johnson, S. H. (1998). Experimental Study of Golf Ball Oblique Impact, Science and Golf III. In Proceedings of the World Science Congress of Golf, 1998.

Jones, I. R. (2002). Is the impact of a golf ball Hertzian. In Science and golf IV. Proceedings of the world scientific congress of golf, Routledge, London (pp. 501-514).

Marquardt, C. (2007). The sam puttlab: Concept and PGA tour data. International Journal of Sports Science & Coaching, 2(1_suppl), 101-120.

Karlsen, J. (2003). Golf putting: An analysis of elite-players technique and performance. Master’s thesis, Norweign University of Sport and Physical Education, Oslo, Norway.

Karlsen, J. (2010). Performance in golf putting.

Karlsen, J., & Nilsson, J. (2007). Club shaft weight in putting accuracy and perception of swing parameters in golf putting. Perceptual and motor skills, 105(1), 29-38.

Karlsen, J., Smith, G., & Nilsson, J. (2008a). The stroke has only a minor influence on direction consistency in golf putting among elite players. Journal of Sports Sciences, 26(3), 243-250.

Karlsen, J., & Nilsson, J. (2008b). Distance variability in golf putting among highly skilled players: The role of green reading. International Journal of Sports Science & Coaching, 3(1_suppl), 71-80.

Koslow, R., & Wenos, D. (1998). Realistic expectations on the putting green within and between days trueness of roll. Perceptual and Motor Skills 87(31), 1441-1442.

Lambeth, J., Brekke, D., & Brunski, J. (2018). Variable Face Milling to Normalize Putter Ball Speed and Maximize Forgiveness. In Multidisciplinary Digital Publishing Institute Proceedings (Vol. 2, No. 6, p. 248).

Lee, T. D., Ishikura, T., Kegel, S., Gonzalez, D., & Passmore, S. (2008). Head-Putter Coordination Patterns in Expert and Less Skilled Golfers, Journal of Motor Behavior, 40(4), 267-272.

Lemons, L. D., Stanczack, M. B., Beasley, D., Cochran, A. J., & Farrally, M. R. (1998, July). The effects of golf ball construction on putting. In Science and golf III, Proceedings of the World Scientific Congress of Golf, St. Andrews, Scotland (pp. 18-22).

LePort-Samzun, C., Trepleton, R., & Strangwood, M. (2002). Fatigue performance of TIG welded age hardening aluminium-based alloy bicycle frame, The Engineering of Sport , 4, 515-522.

Lieberman, B. B. (1990). The effect of impact conditions on golf ball spin rate.Science and Golf, 225-230.

Lieberman, B. B., & Johnson, S. H. (1994). An analytical model for ball-barrier impart, Part 1 and Part 2. In Proceedings of the 1994 World Scientific Congress of Golf, St. Andrews, Scotland (pp. 309-319).

Lindsay, N.M. (2003). Topspin in putters — a study of vertical gear-effect and its dependence on shaft coupling. Sports Engineering 6(2), 81-93.

Lorensen, W.E., & Yamrom, B. (1992). Golf Green Visualization. IEEE computer graphics and applications 12(4), 35-44.

Mackenzie, S. J., & Evans, D. B. (2010). Validity and reliability of a new method for measuring putting stroke kinematics using the TOMI® system. Journal of sports sciences, 28(8), 891-899.

MacPherson, A. C., Collins, D., & Morris, C. (2008). Is what you think what you get? Optimizing mental focus for technical performance, The Sport Psychologist, 22, 288-303.

Maltby, R., n.d. How putter loft works at impact: A technical discussion of skid vs. roll. Available at: www.ralphmaltby.com/274.

Marquardt, C. (2007). The SAM PuttLab. Concept and PGA Tour data. In S. Jenkins (Ed), Annual Review of Golf Coaching 2007,101-114.Essex: Multi Science Publishing.

Marquardt, C., & Mai, N. (1994). A computational procedure for movement analysis in handwriting. Journal of Neuroscience Methods, 52(1), 39-45.

Maw, N., Barber, J. R., & Fawcett, J. N. (1976). The oblique impact of elastic spheres. Wear, 38(1), 101-114.

Maw, N., Barber, J. R., & Fawcett, J. N. (1981). The role of elastic tangential compliance in oblique impact. Journal of Tribology, 103(1), 74-80.

McCloy, A. J., Wallace, E. S., & Otto, S. R. (2006). Iron golf club striking characteristics for male elite golfers. In The Engineering of Sport 6 (pp. 353-358). Springer New York.

McFall, T. A., & Treme, J. (2012). Pandora's groove: analysing the effect of the U-groove ban on PGA Tour golfers' performances and strategies. Applied Economics Letters, 19(8), 763-768.

Menard, S. (1995). An introduction to logistic regression diagnostics. Applied logistic regression analysis, 58-79.

Mindlin, R. D., & Deresiewicz, H. (1954). Thickness‐shear and flexural vibrations of a circular disk. Journal of applied physics, 25(10), 1329-1332.

Monk, S. A., Davis, C. L., Otto, S. R., & Strangwood, M. (2005). Material and surface effects on the spin and launch angle generated from a wedge/ball interaction in golf. Sports Engineering, 8(1), 3-11.

Mullen, R., & Hardy, L. (2000). State anxiety and motor performance: Testing the conscious processing hypothesis. Journal of Sport Sciences, 18, 785-799.

Oatis, D.A., n.d. It's time we put the green back in green speeds. Available at: www.usga.org/course_care/articles/management/greens/it-s-time- we-put-the-green-back-in-green-speed/.

Olson, G. B. (1992). Introduction: martensite in perspective. ASM International, Martensite(USA), 1992,, 1-10.

Paradisis, G., & Rees, J. (2002). Kinematic Analysis of Golf Putting for Expert and Novice Golfers, Proceedings of XVIII International Symposium on Biomechanics in Sports; 2002, 325-8, 2002.

Pelz, D. (1989). Putt like the pros. New York : Harper Collins Publishers.

Pelz, D. (2000). Dave Pelz's putting bible: The complete guide to mastering greens. Doubleday Books.

Penner, A. R. (2002). The physics of putting. Canadian Journal of Physics, 80(2), 83-96.

Perry, S.K. (2002). The proof is in the putting. The physics teacher 40, 411-414.

Pope, J., James, D., Wood, P., & Henrikson, E. (2014). The Effect of Skid Distance on Distance Control in Golf Putting. Procedia Engineering, 72, 642-647.

R&A Rules Limited. (2009). A guide to the rules on clubs and balls. The Royal & Ancient Golf Club of St. Andrews.

Riccio, L. J. (1990). Statistical analysis of the average golfer. in “Science and golf: Proceedings of the first world scientific congress of golf”. In: Cochran, AJ. (Ed.).

Rinkenauer, G., Ulrich, R., & Wing, A. M. (2001). Brief bimanual force pulses: correlations between the hands in force and time. Journal of Experimental Psychology: Human Perception and Performance, 27(6), 1485.

Richardson, A. K., Mitchell, A. C., & Hughes, G. (2015). Reliability of an experimental method to analyse the impact point on a golf ball during putting. Sports biomechanics, 14(2), 206-215.

Richardson, A. K., Mitchell, A. C., & Hughes, G. (2018). The effect of movement variability on putting proficiency during the golf putting stroke. International Journal of Sports Science & Coaching, 13(4), 590-597.

Schmidt, E., Roberts, J., & Rothberg, S. (2006). Time-Resolved Measurements of Grip Force during a Golf Shot, The Engineering of Sports, 6, 57-62.

Sherwin, I. A., & Kenny, I. C. (2013). An examination of putting movement and performance variability using standard, belly and long-handled putters.

Sim, M., & Kim, J. U. (2010). Differences between experts and novices in kinematics and accuracy of golf putting, Human Movement Science, 29, 932-946.

Smith, D., & Holmes, P. (2004). The effect of imagery modality on golf putting performance. Journal of Sport and Exercise Psychology, 26, 385-395.

Sullivan, M. J., & Weiss, R. A. (1994). Novel high acid ionomers for golf ball cover applications. In Science and Golf II: Proceedings of the Second World Scientific Congress of Golf. (383-389). London : E & FN Spon.

Sullivan, M. J., & Melvin, T. (1994). The relationship between golf ball construction and performance. Science and Golf II, 334-339.

Tierney, D. E., & Coop, R. H. (1998). A bivariate probability model for putting proficiency. In Science and Golf III: Proceedings of the 1998 World Scientific Congress of Golf (pp. 385-394). Champaign, IL: Human Kinetics.

Toner, J., & Moran, A. (2011). The effects of conscious processing on golf putting proficiency and kinematics. Journal of sports sciences, 29(7), 673-683.

Ujihashi, S. (1994). Measurement of dynamic characteristics of golf balls and identification of their mechanical models. In Science and Golf II: Proceedings of the 1994 World Scientific Congress of Golf (pp. 302-308).

Van Lier, W. H., Van Der Kamp, J., & Savelsbergh, G. J. P. (2011). Perception and Action in Golf Putting: Skill Differences Reflect Calibration, Journal of Sport & Exercise Psychology, 2011, 33, 349-369.

Wilson, M., & Pearcy, R. C. (2009). Visuomotor control of straight and breaking putts, Perceptual and Motor Skills, 109, 1-8.

Wiren, G. (1990). PGA teaching Manual: The art and science of golf instruction. Palm Beach Gardens, FL: PGA of America.

Wu, Y. L., Huang, C. F., Marquardt, C., Yu, L. C., & Lee, S. W. (2012). The influence of adjustable putter head weighting on the stroke. In ISBS-Conference Proceedings Archive.

Wu, Y. L., Huang, C. F., Liu, Y. C., & Marquart, C. (2013, September). GOLF PUTTING GRIP DESIGN INFLUENCES ON PUTTING KINEMATICS. In ISBS-Conference Proceedings Archive.

Wu, Y. L., Huang, C. F., Liu, Y. C., Marquardt, C., & Chen, P. C. (2014, October). LEVERAGING SPORTING EQUIPMENT BALANCE AND WEIGHT DISTRUBUTION INFLUENCE ON PUTTING KINEMATICS–A STUDY ON COUNTER-BALANCED PUTTER DESIGN. In ISBS-Conference Proceedings Archive.

Wu, Y. L., Huang, C. F., Marquardt, C., & Wang, H. T. (2020). Putting Performance and Kinematics Differ with Skill Level in Female Golfers. The Open Sports Sciences Journal, 13(1).

Yun, H. (2013). USGA INTRODUCES UPDATED STIMPMETER:The Tool For Testing Green Speeds Promotes Consistent Putting Surfaces, Which Enhance Playing Experience, retreieved on 2014/11/27 from http://www.usga.org/news/2013/January/USGA-Introduces-Updated-Stimpmeter/.