The triskelion software program has been developed by using the analytical elastic model. The MATLAB environment is a flexible means for developing complex algorithms and functions. The MATLAB workspace is also very useful for the type of modelling research work being presented in this thesis. The nomenclature of the input parameters to execute the program is given in table (4.2).
The whole program was written as a collection of functions, each with aim, pre-condition and post-condition to reflect one sequential step in the enhanced linear elastic model in
Main Function
Model Input(dz,dthetax, dthetay, a, l,w,t,E,alpha and beta angles)
Function to computer arms deflection
In a body fix frame of co-ordinate Function to computer stiffness matix
Function to computer orientation of beta beta angle for three beams
Function to compute beams deflection in a body fix-frame of co-ordinate
Function to compute beams forces and Moments in a body fix-frame of
co-ordinates
Function to compute beams forces and moments in a global-frame of co-ordinates
Function to compute the sum of forces in global frame of reference
Function to computer stress and strain
in a gobal co-ordinates
Function to compute to stiffness and
and in global co-ordinates
detail of the computational schema and codes for triskelion software program, have been described in the appendix C.
During the development phase, the execution of a function was tested by manually placing appropriate input parameters into the MATLAB interpretive workplace and then calling it, standing alone, from the workplace. The computed results were compared with the hand calculated results. The same procedure was adopted for every function of the triskelion software program.
At the last stage of the development, when all codes for all required functions were completed, the codes for the main function was written by defining all input parameters (δz, θx, θy, a, l, w, t, E, α1, α2, α3, β1, β2, &β3). Each function in the main program
is called in the right order shown in the dependance diagram, figure 4.2.
The first three input parameters (δz, θx & θy, ) represent displacements externally imposed upon three degree of freedom of the platform; they are respectively a translation along thez-axis and small angle rotations about thex−and y-axes. Note that for a force transfer artefact expectsδzto be the desire input, with the rotations being parasitic motions. However, in the case of a microprobe,x−y−zmotions at the probe tip correspond directly to these inputs at the platform, since the model is linear, the actual choice of value for these parameters is of little consequence, but here value representative of typical applications are always used. The remaining set of input parameters define geometries of the platform, beam and material constant parameters, which are necessary for the execution of all functions that compute the enhanced linear elastic model. The triskelion software is considered to be a good tool for predicting the stiffness of force artefacts and micro probe suspension artefact over short deflection range prior to their fabrication processes.
4.4.1 Triskelion software program verification
Before starting the numerical experiments, the consistency and robustness of the triskelion software program was tested using a simple input values at the platform that can compared
1. The fist consistency trial was carried out by using input parameters δz = 1×10−5 and θx &θy = 0, and values of other parameters as given in table 4.2. The program was computed for triskelion force artefacts with 60◦ elbow angle. Subsequently, this experiment was repeated for all other triskelion force artefacts and input specifications given in table 4.2, The same value of stiffnesskz was computed by the program in all cases by forcingθx =θy = 0, the platform undergoes pure z-translations and each of its arm moves the same distance. Thus the end of each suspension beam is subject only to, in its body-fixed frame,z-shift andy-rotation and these are identical for each beam. If the beam geometries and material remain the same, so does the associated stiffness matrix, consequently the end-force and end-moment. Hence the value of kz remains same for all triskelion force artefacts, having different elbow angles if the design parameters are unchanged.
2. The second trial was carried out by havingθx= 1×10−3, δz&θy = 0 by keeping the same input values as above and a 60◦ elbow angle. The program respondsMxas finite and positive andFz= 0. Similarly, trial was repeated for all triskelion force artefacts and input specifications given in Table (4.2) and the same result was found i.e. positive Mx and Fz = 0. This follows the physical expectation that pure rotation of the platform about thex-axis should require purely asx-axis moment (other than possible parasitic effects not accessible to a linear elastic model). However, the moment is not necessarily independent of the elbow angle because the tilting platform can induce torsional effects in the beams.
3. The third numerical experiment was carried out by usingθy = 1×10−3, δz &θx= 0 while other being the same as trial 2. The program reportsMy as finite and positive, Mx = 0 and Fz = 0 in all cases tested. This meet the physical expectation that by symmetry, the simple torsional behaviour of the platform should be the same on any axis.
4. The fourth numerical experiment was carried out by using θx or θy = 1×10−3 and δz= 0 for all triskelion force artefacts by keeping the same value of parameters given in table 4.2. The program computes Mx = My and Fz = 0 for all triskelion force
artefacts, which have different elbow angles. This test confirms that no unintended cross-axis twist effects have been introduced into the program
5. The final trial was carried out by usingδz= 1×10−5 &θx= 1−3 andθy = 0 but was otherwise the same as trial 4. The program computed the same value of Fz for all triskelion force artefacts, but with different values ofMxandMx= 0 . The parameter θxgenerates rotation about the x-axis in the plane of platform and hence the program predicts the different values ofMx for all triskelion force artefacts with different elbow angles. this test confirms there is no unexpected cross-talk between translational and rotational inputs.
All the above testing experiments confirm the robustness of the triskelion software program