The Space Curve Mesh Equation and Its Kinematics Experiment 12th IFToMM World Congress, Besançon, France, June 18–21 2007. 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

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.

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.

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

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.

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

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

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

The mesh equation: is the relative velocity in tangent point

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:

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

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.

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:

the space curve equation of driven tine:

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

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

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 :

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

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

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

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

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

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.

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

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

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

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.

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.

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

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.

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

Thank you!