Study: estimation of the required joint stroke
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@ -613,6 +613,64 @@ data2orgtable([1e6*L_min, 1e6*L_max, 1e6*(min(min(rs)))], {}, {'=L_min= [$\mu m$
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*** TODO Do that by slice :noexport:
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using this function https://fr.mathworks.com/help/matlab/ref/contour3.html
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* Estimation of the Joint required Stroke
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** Introduction :ignore:
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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#+begin_src matlab :results none :exports none
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simulinkproject('../');
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#+end_src
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** Example of the initialization of a Stewart Platform
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Let's first define the Stewart Platform Geometry.
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#+begin_src matlab
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stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 150e-3);
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stewart = generateGeneralConfiguration(stewart);
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stewart = computeJointsPose(stewart);
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As_init = stewart.geometry.As;
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#+end_src
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#+begin_src matlab
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Tx_max = 50e-6; % Translation [m]
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Ty_max = 50e-6; % Translation [m]
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Tz_max = 50e-6; % Translation [m]
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#+end_src
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#+begin_src matlab
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Ps = [2*(dec2bin(0:3^2-2,3)-'0')-1].*[Tx_max Ty_max Tz_max];
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#+end_src
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#+begin_src matlab
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flex_ang = zeros(size(Ps, 1), 6);
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for Ps_i = 1:size(Ps, 1)
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stewart.geometry.FO_M = [0; 0; 90e-3] + Ps(Ps_i, :)';
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stewart = generateGeneralConfiguration(stewart);
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stewart = computeJointsPose(stewart);
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flex_ang(Ps_i, :) = acos(sum(As_init.*stewart.geometry.As));
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end
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#+end_src
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And the maximum bending of the flexible joints is: (in [mrad])
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#+begin_src matlab :results replace value
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1e3*max(max(abs(flex_ang)))
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#+end_src
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#+RESULTS:
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: 0.90937
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* Functions
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<<sec:functions>>
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** =computeJacobian=: Compute the Jacobian Matrix
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@ -951,6 +951,8 @@ This Matlab function is accessible [[file:../src/initializeCylindricalStruts.m][
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#+begin_src matlab
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arguments
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stewart
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args.type_F char {mustBeMember(args.type_F,{'cylindrical', 'none'})} = 'cylindrical'
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args.type_M char {mustBeMember(args.type_M,{'cylindrical', 'none'})} = 'cylindrical'
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args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
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args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
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args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
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@ -995,7 +997,12 @@ This Matlab function is accessible [[file:../src/initializeCylindricalStruts.m][
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:UNNUMBERED: t
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:END:
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#+begin_src matlab
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switch args.type_M
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case 'cylindrical'
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stewart.struts_M.type = 1;
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case 'none'
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stewart.struts_M.type = 2;
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end
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stewart.struts_M.I = I_M;
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stewart.struts_M.M = Msm;
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@ -1004,7 +1011,12 @@ This Matlab function is accessible [[file:../src/initializeCylindricalStruts.m][
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#+end_src
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#+begin_src matlab
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switch args.type_F
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case 'cylindrical'
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stewart.struts_F.type = 1;
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case 'none'
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stewart.struts_F.type = 2;
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end
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stewart.struts_F.I = I_F;
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stewart.struts_F.M = Fsm;
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@ -1237,10 +1249,83 @@ A simplistic model of such amplified actuator is shown in Figure [[fig:amplified
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stewart.actuators.Cr = args.Cr;
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stewart.actuators.K = K;
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stewart.actuators.C = K;
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stewart.actuators.C = C;
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#+end_src
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** =initializeJointDynamics=: Add Stiffness and Damping properties for spherical joints
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** TODO =initializeFlexibleStrutDynamics=: Model each strut with a flexible element
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:PROPERTIES:
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:header-args:matlab+: :tangle ../src/initializeFlexibleStrutDynamics.m
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:header-args:matlab+: :comments none :mkdirp yes :eval no
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:END:
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<<sec:initializeFlexibleStrutDynamics>>
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This Matlab function is accessible [[file:../src/initializeFlexibleStrutDynamics.m][here]].
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*** Function description
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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#+begin_src matlab
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function [stewart] = initializeFlexibleStrutDynamics(stewart, args)
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% initializeFlexibleStrutDynamics - Add Stiffness and Damping properties of each strut
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%
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% Syntax: [stewart] = initializeFlexibleStrutDynamics(args)
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%
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% Inputs:
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% - args - Structure with the following fields:
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% - K [nxn] - Vertical stiffness contribution of the piezoelectric stack [N/m]
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% - M [nxn] - Vertical damping contribution of the piezoelectric stack [N/(m/s)]
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% - xi [1x1] - Vertical (residual) stiffness when the piezoelectric stack is removed [N/m]
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% - step_file [6x1] - Vertical (residual) damping when the piezoelectric stack is removed [N/(m/s)]
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%
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% Outputs:
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% - stewart - updated Stewart structure with the added fields:
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#+end_src
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*** Optional Parameters
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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#+begin_src matlab
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arguments
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stewart
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args.K double {mustBeNumeric} = zeros(6,6)
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args.M double {mustBeNumeric} = zeros(6,6)
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args.H double {mustBeNumeric} = 0
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args.n_xyz double {mustBeNumeric} = zeros(2,3)
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args.xi double {mustBeNumeric} = 0.1
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args.step_file char {} = ''
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end
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#+end_src
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*** Compute the axial offset
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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#+begin_src matlab
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stewart.actuators.ax_off = (stewart.geometry.l(1) - args.H)/2; % Axial Offset at the ends of the actuator
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#+end_src
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*** Populate the =stewart= structure
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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#+begin_src matlab
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stewart.actuators.type = 3;
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stewart.actuators.Km = args.K;
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stewart.actuators.Mm = args.M;
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stewart.actuators.n_xyz = args.n_xyz;
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stewart.actuators.xi = args.xi;
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stewart.actuators.step_file = args.step_file;
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stewart.actuators.K = args.K(3,3); % Axial Stiffness
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#+end_src
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** TODO =initializeJointDynamics=: Add Stiffness and Damping properties for spherical joints
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:PROPERTIES:
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:header-args:matlab+: :tangle ../src/initializeJointDynamics.m
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:header-args:matlab+: :comments none :mkdirp yes :eval no
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@ -1291,8 +1376,8 @@ This Matlab function is accessible [[file:../src/initializeJointDynamics.m][here
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#+begin_src matlab
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arguments
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stewart
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args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p'})} = 'universal'
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args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p'})} = 'spherical'
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args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p', 'flexible'})} = 'universal'
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args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p', 'flexible'})} = 'spherical'
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args.Kf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
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args.Cf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
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args.Kt_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
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@ -1301,6 +1386,16 @@ This Matlab function is accessible [[file:../src/initializeJointDynamics.m][here
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args.Cf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
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args.Kt_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
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args.Ct_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
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args.K_M double {mustBeNumeric} = zeros(6,6)
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args.M_M double {mustBeNumeric} = zeros(6,6)
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args.n_xyz_M double {mustBeNumeric} = zeros(2,3)
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args.xi_M double {mustBeNumeric} = 0.1
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args.step_file_M char {} = ''
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args.K_F double {mustBeNumeric} = zeros(6,6)
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args.M_F double {mustBeNumeric} = zeros(6,6)
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args.n_xyz_F double {mustBeNumeric} = zeros(2,3)
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args.xi_F double {mustBeNumeric} = 0.1
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args.step_file_F char {} = ''
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end
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#+end_src
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@ -1318,6 +1413,8 @@ This Matlab function is accessible [[file:../src/initializeJointDynamics.m][here
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stewart.joints_F.type = 3;
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case 'spherical_p'
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stewart.joints_F.type = 4;
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case 'flexible'
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stewart.joints_F.type = 5;
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end
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switch args.type_M
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@ -1329,6 +1426,8 @@ This Matlab function is accessible [[file:../src/initializeJointDynamics.m][here
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stewart.joints_M.type = 3;
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case 'spherical_p'
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stewart.joints_M.type = 4;
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case 'flexible'
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stewart.joints_M.type = 5;
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end
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#+end_src
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@ -1371,7 +1470,6 @@ Rotational Stiffness
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stewart.joints_F.Kt = args.Kf_F;
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#+end_src
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Rotational Damping
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#+begin_src matlab
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stewart.joints_M.Cf = args.Cf_M;
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@ -1381,6 +1479,26 @@ Rotational Damping
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stewart.joints_F.Ct = args.Cf_F;
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#+end_src
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*** Stiffness and Mass matrices for flexible joint
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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#+begin_src matlab
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stewart.joints_F.M = args.M_F;
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stewart.joints_F.K = args.K_F;
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stewart.joints_F.n_xyz = args.n_xyz_F;
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stewart.joints_F.xi = args.xi_F;
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stewart.joints_F.xi = args.xi_F;
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stewart.joints_F.step_file = args.step_file_F;
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stewart.joints_M.M = args.M_M;
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stewart.joints_M.K = args.K_M;
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stewart.joints_M.n_xyz = args.n_xyz_M;
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stewart.joints_M.xi = args.xi_M;
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stewart.joints_M.step_file = args.step_file_M;
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#+end_src
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** =initializeInertialSensor=: Initialize the inertial sensor in each strut
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:PROPERTIES:
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:header-args:matlab+: :tangle ../src/initializeInertialSensor.m
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Binary file not shown.
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@ -40,4 +40,4 @@ stewart.actuators.Kr = args.Kr;
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stewart.actuators.Cr = args.Cr;
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stewart.actuators.K = K;
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stewart.actuators.C = K;
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stewart.actuators.C = C;
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@ -27,6 +27,8 @@ function [stewart] = initializeCylindricalStruts(stewart, args)
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arguments
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stewart
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args.type_F char {mustBeMember(args.type_F,{'cylindrical', 'none'})} = 'cylindrical'
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args.type_M char {mustBeMember(args.type_M,{'cylindrical', 'none'})} = 'cylindrical'
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args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
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args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
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args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
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@ -56,14 +58,24 @@ for i = 1:6
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1/2 * Msm(i) * Msr(i)^2]);
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end
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stewart.struts_M.type = 1;
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switch args.type_M
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case 'cylindrical'
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stewart.struts_M.type = 1;
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case 'none'
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stewart.struts_M.type = 2;
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end
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stewart.struts_M.I = I_M;
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stewart.struts_M.M = Msm;
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stewart.struts_M.R = Msr;
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stewart.struts_M.H = Msh;
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stewart.struts_F.type = 1;
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switch args.type_F
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case 'cylindrical'
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stewart.struts_F.type = 1;
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case 'none'
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stewart.struts_F.type = 2;
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end
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stewart.struts_F.I = I_F;
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stewart.struts_F.M = Fsm;
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@ -29,8 +29,8 @@ function [stewart] = initializeJointDynamics(stewart, args)
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arguments
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stewart
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args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p'})} = 'universal'
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args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p'})} = 'spherical'
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args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p', 'flexible'})} = 'universal'
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args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p', 'flexible'})} = 'spherical'
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args.Kf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
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args.Cf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
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args.Kt_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
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@ -39,6 +39,16 @@ arguments
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args.Cf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
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args.Kt_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
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args.Ct_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
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args.K_M double {mustBeNumeric} = zeros(6,6)
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args.M_M double {mustBeNumeric} = zeros(6,6)
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args.n_xyz_M double {mustBeNumeric} = zeros(2,3)
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args.xi_M double {mustBeNumeric} = 0.1
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args.step_file_M char {} = ''
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args.K_F double {mustBeNumeric} = zeros(6,6)
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args.M_F double {mustBeNumeric} = zeros(6,6)
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args.n_xyz_F double {mustBeNumeric} = zeros(2,3)
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args.xi_F double {mustBeNumeric} = 0.1
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args.step_file_F char {} = ''
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end
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switch args.type_F
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@ -50,6 +60,8 @@ switch args.type_F
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stewart.joints_F.type = 3;
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case 'spherical_p'
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stewart.joints_F.type = 4;
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case 'flexible'
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stewart.joints_F.type = 5;
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end
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switch args.type_M
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@ -61,6 +73,8 @@ switch args.type_M
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stewart.joints_M.type = 3;
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case 'spherical_p'
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stewart.joints_M.type = 4;
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case 'flexible'
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stewart.joints_M.type = 5;
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end
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stewart.joints_M.Kx = zeros(6,1);
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@ -90,3 +104,16 @@ stewart.joints_M.Ct = args.Cf_M;
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stewart.joints_F.Cf = args.Cf_F;
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stewart.joints_F.Ct = args.Cf_F;
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stewart.joints_F.M = args.M_F;
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stewart.joints_F.K = args.K_F;
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stewart.joints_F.n_xyz = args.n_xyz_F;
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stewart.joints_F.xi = args.xi_F;
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stewart.joints_F.xi = args.xi_F;
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stewart.joints_F.step_file = args.step_file_F;
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stewart.joints_M.M = args.M_M;
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stewart.joints_M.K = args.K_M;
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stewart.joints_M.n_xyz = args.n_xyz_M;
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stewart.joints_M.xi = args.xi_M;
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stewart.joints_M.step_file = args.step_file_M;
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