1. Design of Experiment Group member: Li Zheran Xu Zan She Manrong Lei Chen

2. Content : MMotivation LLiterature review DDesign of Experiment IImplementation RRestrictions 2

3. Motivation  Find out the main effect on spinning top  Design a model between the effect and the response  Help understand the work principle of spinning top 3

4. Content :  Motivation  Literature review  Design of Experiment  Implementation  Restrictions 4

5. Literature review  The history of spinning-top: ① 明代刘侗、于奕正《帝经 物略 · 二春场》载 : “ 陀螺者， 木制，如小空钟，中实而 无柄。绕以鞭之绳，卓于 地，争制其鞭 ……” 。 ② 1852 年, 博科 (Foucault) 首 先将高速旋转的刚体称为 陀螺。 Wooden gyro Clockwork gyro Rotating handle gyro 5

6. Literature review  The process of turning spinning-top: 6

7. Literature review  The process of turning spinning-top: 7

8. Content :  Motivation  Literature review  Design of Experiment  Implementation  Restrictions 8

9. Design of Experiment Factor Decomposition Implementation of the experiments Data analysis The results of the design 9

10. Factor Decomposition  Response Variable:  Response Variable: Slewing time  Control variable: ① Ground surface （ cement / plastic / ceramic ） ② Height （ low / high ） ③ Weight （ light / heavy ）  Fixed variables:  Fixed variables: Force （ held constant ）  Nuisance factor: ① Surface homogeneous ② Wind speed 10

11. Factor Level Definition Control Variable CodeLevelsLevel Code Ground SurfaceA Cement Ground1 Plastic Ground(playground)2 Ceramic Ground3 HeightB Low(H=10cm)1 High(H=20cm)2 Gyro WeightC Light1 Heavy(with plasticine)2 11

12. Preliminary Experiment Choose rotating handle gyro to do the preliminary experiment to control the fixed factor Ground Surface cement Height H=10cm Weight light 12

13. Control the fixed factor 13

14. Control the fixed factor 14

15. Content :  Motivation  Literature review  Design of Experiment  Implementation  Restrictions 15

16. Implementation 1:cement 2:plastic 3:ceramic A: ground surface 1:H=10cm 2:H=20cm B: height 1:light 2:heavy C: weight 16

17. Implementation Full Factorial Design 17

18. Data analysis Significant effect A: type of ground surface C: the weight of the gyro No significant effect B: the height 18

19. Data analysis （ cont. ） No interaction effect A and B B and C Significant effect A and C On the ceramic ground, the difference is bigger. 19

20. Data analysis （ cont. ） Normality assumption Normal probability plot √ Histogram √ Equal variance assumption Residual VS fitted value ╳ 20

21. Slewing Time 的方差分析，在检验中使用调整的 SS 来源 自由度 Seq SS Adj SS Adj MS F P A 2 7719.96 7719.96 3859.98 300.64 0.000 B 1 2.05 2.05 2.05 0.16 0.691 C 1 1189.04 1189.04 1189.04 92.61 0.000 A*B 2 2.75 2.75 1.38 0.11 0.899 A*C 2 575.56 575.56 287.78 22.41 0.000 B*C 1 6.21 6.21 6.21 0.48 0.490 A*B*C 2 18.10 18.10 9.05 0.70 0.499 误差 48 616.28 616.28 12.84 合计 59 10129.95 S = 3.58317 R-Sq = 93.92% R-Sq （调整） = 92.52% 项 系数 系数标准误 T P 常量 19.6983 0.4626 42.58 0.000 A 1 -4.8033 0.6542 -7.34 0.000 2 -10.8533 0.6542 -16.59 0.000 B 1 -0.1850 0.4626 -0.40 0.691 C 1 4.4517 0.4626 9.62 0.000 A*B 1 1 0.0400 0.6542 0.06 0.951 2 1 0.2400 0.6542 0.37 0.715 A*C 1 1 -0.6967 0.6542 -1.06 0.292 2 1 -3.3967 0.6542 -5.19 0.000 B*C 1 1 0.3217 0.4626 0.70 0.490 A*B*C 1 1 1 -0.6067 0.6542 -0.93 0.358 2 1 1 -0.1167 0.6542 -0.18 0.859 21

22. Another experiment 1:cement 2:plastic 3:ceramic A: ground surface 1:H=30cm 2:H=1m B: height 1:light 2:heavy C: weight Clockwork gyro 22

23. Data analysis 23

24. Data analysis 24

25. Slewing Time 的方差分析，在检验中使用调整的 SS 来源 自由度 Seq SS Adj SS Adj MS F P A 2 273.476 308.292 154.146 291.91 0.000 B 1 0.089 0.081 0.081 0.15 0.696 C 1 38.019 64.031 64.031 121.26 0.000 A*B 2 0.537 0.113 0.056 0.11 0.899 A*C 2 29.137 29.028 14.514 27.49 0.000 B*C 1 0.136 0.482 0.482 0.91 0.344 A*B*C 2 0.973 0.973 0.487 0.92 0.405 误差 48 25.347 25.347 0.528 合计 59 367.714 S = 0.726677 R-Sq = 93.11% R-Sq （调整） = 91.53% 项 系数 系数标准误 T P 常量 19.2759 0.4119 46.80 0.000 A 1 -4.7976 0.5450 -8.80 0.000 2 -10.5211 0.4967 -21.18 0.000 B 1 -0.1617 0.4119 -0.39 0.696 C 1 4.5355 0.4119 11.01 0.000 A*B 1 1 0.0217 0.5450 0.04 0.968 2 1 0.2241 0.4967 0.45 0.654 A*C 1 1 -0.7190 0.5450 -1.32 0.193 2 1 -3.5094 0.4967 -7.07 0.000 B*C 1 1 0.3936 0.4119 0.96 0.344 A*B*C 1 1 1 -0.6616 0.5450 -1.21 0.231 2 1 1 -0.2219 0.4967 -0.45 0.657 25

26. The results of the design  Main effect: Ground surface & weight with 95% confidence  Ground surface effect: Ceramic material increases the slewing time  Weight effect: Lighter gyro increases the slewing time 26

27. Content :  Motivation  Literature review  Design of Experiment  Implementation  Restrictions 27

28. Restrictions on the experiment Force control: Force control: Though we have practice to keep force constant, there is still personal error. Difficult to control the weight: Difficult to control the weight: To control the weight, we choose to cover plasticine to plus weight. Data acquisition: Data acquisition: Each run we use stopwatch to record data, which may have measuring error. Wearing restriction: Wearing restriction: With the increasing of run times, the gyro wearing increases. 28

30. Thank you for listening Q&A 30