1. The Space Curve Mesh Equation and Its Kinematics Experiment
12th IFToMM World Congress, Besançon, France, June 18–
The Space Curve Mesh Equation and Its Kinematics Experiment
By Prof. Yang-zhi Chen
From South China University of Technology
Guangzhou,510640,P.R.China

2. Ⅰ. Introduction
We invented Micro-Elastic-Mesh-Wheel-Transmission (MEMWT)
Use:
Transmitting power and locomotion between two shafts, the axes of which are upright and cross in micro space.
Advantages:
(1) The structure is simplified ;
(2) The dimension is reduced ;
(3) The cost is much lowered.

3. Ⅰ. Introduction Differences Conventional mesh transmission:
gear transmission, worm transmission, etc;
space surface meshing;
used for power transmission in industry.
MEMWT:
space curve meshing;
used for mini-power and locomotion transmission in micro device.

4. Ⅱ.The Principle of MEMWT
Components: driver, driven wheel, driving tine and driven tine.
Driving tine
Driver
Driven wheel
Driven tine
Micro motor
Fig.1 the principle of MEMWT
Back to movies
Back to introduction

5. Ⅲ.The Space Curve Mesh Equation (SCME)
Supposed:
The tine could be taken as rigid tine.
Reasons:
a) small acted force ;
b) its deformation is very small.

6. A. The basic space curve mesh equation
is tangent vector
is principal normal vector
is assisted vector
Fig.2 the space curve

7. The coordinates of mesh
Fig.3
The coordinates of mesh
Back

8. space curve equation: The tangent vector
Where, k is curvature of space curve, and

9. The mesh equation:
is the relative velocity in tangent point

10. The equation of space curve of driving tine in coordinate system S1is:
Where, t is a parameter of curve.
The expression of principal normal vector in coordinate S1 is:
The relative velocity v12 is expressed by:

11. According to the mesh equation We can get the basic space curve mesh equation:
Back

12. B. The space curve equation of driven tine
If mesh is single degree of freedom, there is only independent locomotion parameter, and other parameters are its functions.

13. Transfer the space curve equation in the coordinate system S1 to that in the coordinate system S2,
Supposing that the space curve equation of driving tine is known, the space curve equation of driven tine could be given:

14. the space curve equation of driven tine:

15. C. Application
Supposed the space curve of driving tine is a helical line,
The expression of the space curve of driving tine in S1 is

16. the principal normal vector of the helical line:
a helical line Eq:
the space curve equation of driven tine:

17. Example: Supposed the parameters of a transmission mechanism are: a = 5.0; b =18.0; m = 5.0; n =3.0; i21=1:4, viz.,
the space curve equation of driving tine :
the space curve equation of driven tine :

18. The space curve of driving tine
The space curve of driven tine
Fig.4 the space mesh curve

19. Ⅳ. The Kinematics Experiment of MEMWT 1
Ⅳ.The Kinematics Experiment of MEMWT 1. The preparation of transmission pairs
The die of driving tine (b) The die of driven tine
Fig5. The dies which are used to make the driving tine
and driven tine

20. 1. The preparation of transmission pairs
(a) Driver (b) Driven wheel
Fig. The photo of driving wheel and driven wheel
Back

21. 2. The test rig of kinematics performance
Bearer 2. Load cell 3. Driving wheel 4. Driven wheel
5.Elastic tine 6. Driver 7. DC motor
8. Three-dimensional flat 9. Rotary encoder
(a) The structure of the experiment table

22. 2. The test rig of kinematics performance
(b) The photo of the experiment table
Fig. The performance testing table for MEMWT

23. 3. Testing results
3.1 The instantaneous transmission ratio of a couple of tines
Testing tasks:
to measure instantaneous transmission ratio and
average transmission ratio.
Testing conditions:
The voltage of DC motor is 8V;The diameter of
driving wheel is 35mm;the friction coefficient
between driving wheel and load cell is 0.15.

24. 3.1 The instantaneous transmission ratio of a couple of tines
Average transmission ratio: 3.88
Fig. 8. The instantaneous transmission ratio
of a couple of tine
(Resistance torsion: 0gmm)
Back

25. Back Average transmission ratio: 5.06
Fig.9 The instantaneous transmission ratio
of a couple of tine
(Resistance torsion: 28.9gmm)
Average transmission ratio: 5.64
Fig.10 The instantaneous transmission ratio
of a couple of tine
(Resistance torsion: 86.6gmm)
Back

26. 3.2 The instantaneous transmission ratio while multi-tines meshing continuously
Average transmission ratio: 4.02
Fig.11 The instantaneous transmission ratio
of multi-tines

27. 4. Analysis of testing results
1) the instantaneous transmission ratio relates directly to
transmission load while a couple of tines meshing.
2) The testing result of average transmission ratio is approximate to the theoretical value, proving that the space curve
equation of driven tine is correct.
3) The instantaneous transmission ratio appears periodic
fluctuation while multi-tines meshing continuously.
4) When overload transmission takes place (where the load
is 86.6gmm), transmission is fail.

28. The reasons for the deficiency of testing results:
1) the method of making specimen is non-standard;
2) the driving tines and driven tines couldn’t be all distributed evenly by hand work.

29. Expectation: elastic space curve mesh theory its critical loading
Manufacture technics
Experiment rule
Theory optimization

30. Conclusion:
The basic space curve mesh equation (SCME) has been correctly deduced.
The testing results are approximate to the theoretical values proving the SCME.
The deficiency needs to be overcome by further theoretical and experimental study
including elastic space curve mesh theory and manufacturing technology.

31. Simulation of MEMWT by Pro-E
According to Fig.1
Driving Device for Micro Robot In-pipe using MEMWT

32. Thank you!