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< h1 class = "title" > Stewart Platform - Dynamics Study< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#org7743c04" > 1. Compare external forces and forces applied by the actuators< / a >
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< ul >
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< li > < a href = "#orgc730bef" > 1.1. Comparison with fixed support< / a > < / li >
< li > < a href = "#orgefde538" > 1.2. Comparison with a flexible support< / a > < / li >
< li > < a href = "#org53765b8" > 1.3. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgb6a1ef7" > 2. Comparison of the static transfer function and the Compliance matrix< / a >
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< ul >
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< li > < a href = "#org3f1c253" > 2.1. Analysis< / a > < / li >
< li > < a href = "#orga9eb2fd" > 2.2. Conclusion< / a > < / li >
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< / li >
< / ul >
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< / div >
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< div id = "outline-container-org7743c04" class = "outline-2" >
< h2 id = "org7743c04" > < span class = "section-number-2" > 1< / span > Compare external forces and forces applied by the actuators< / h2 >
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< div class = "outline-text-2" id = "text-1" >
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< p >
In this section, we wish to compare the effect of forces/torques applied by the actuators with the effect of external forces/torques on the displacement of the mobile platform.
< / p >
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< / div >
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< h3 id = "orgc730bef" > < span class = "section-number-3" > 1.1< / span > Comparison with fixed support< / h3 >
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< div class = "outline-text-3" id = "text-1-1" >
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< p >
Let’ s generate a Stewart platform.
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, < span class = "org-string" > 'H'< / span > , 90e< span class = "org-type" > -< / span > 3, < span class = "org-string" > 'MO_B'< / span > , 45e< span class = "org-type" > -< / span > 3);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
stewart = initializeJointDynamics(stewart, < span class = "org-string" > 'type_F'< / span > , < span class = "org-string" > 'universal_p'< / span > , < span class = "org-string" > 'type_M'< / span > , < span class = "org-string" > 'spherical_p'< / span > );
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
stewart = initializeInertialSensor(stewart, < span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'none'< / span > );
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< / pre >
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< p >
We don’ t put any flexibility below the Stewart platform such that < b > its base is fixed to an inertial frame< / b > .
We also don’ t put any payload on top of the Stewart platform.
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > ground = initializeGround(< span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'none'< / span > );
payload = initializePayload(< span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'none'< / span > );
controller = initializeController(< span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'open-loop'< / span > );
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< / pre >
< / div >
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< p >
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The transfer function from actuator forces \(\bm{\tau}\) to the relative displacement of the mobile platform \(\mathcal{\bm{X}}\) is extracted.
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< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Options for Linearized< / span > < / span >
options = linearizeOptions;
options.SampleTime = 0;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
mdl = < span class = "org-string" > 'stewart_platform_model'< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Controller'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Actuator Force Inputs [N]< / span >
io(io_i) = linio([mdl, < span class = "org-string" > '/Relative Motion Sensor'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Position/Orientation of {B} w.r.t. {A}< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize(mdl, io, options);
G.InputName = {< span class = "org-string" > 'F1'< / span > , < span class = "org-string" > 'F2'< / span > , < span class = "org-string" > 'F3'< / span > , < span class = "org-string" > 'F4'< / span > , < span class = "org-string" > 'F5'< / span > , < span class = "org-string" > 'F6'< / span > };
G.OutputName = {< span class = "org-string" > 'Edx'< / span > , < span class = "org-string" > 'Edy'< / span > , < span class = "org-string" > 'Edz'< / span > , < span class = "org-string" > 'Erx'< / span > , < span class = "org-string" > 'Ery'< / span > , < span class = "org-string" > 'Erz'< / span > };
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< / pre >
< / div >
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< p >
Using the Jacobian matrix, we compute the transfer function from force/torques applied by the actuators on the frame \(\{B\}\) fixed to the mobile platform:
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > Gc = minreal(G< span class = "org-type" > *< / span > inv(stewart.kinematics.J< span class = "org-type" > '< / span > ));
Gc.InputName = {< span class = "org-string" > 'Fnx'< / span > , < span class = "org-string" > 'Fny'< / span > , < span class = "org-string" > 'Fnz'< / span > , < span class = "org-string" > 'Mnx'< / span > , < span class = "org-string" > 'Mny'< / span > , < span class = "org-string" > 'Mnz'< / span > };
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< / pre >
< / div >
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< p >
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We also extract the transfer function from external forces \(\bm{\mathcal{F}}_{\text{ext}}\) on the frame \(\{B\}\) fixed to the mobile platform to the relative displacement \(\mathcal{\bm{X}}\) of \(\{B\}\) with respect to frame \(\{A\}\):
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< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Disturbances'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > , [], < span class = "org-string" > 'F_ext'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % External forces/torques applied on {B}< / span >
io(io_i) = linio([mdl, < span class = "org-string" > '/Relative Motion Sensor'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Position/Orientation of {B} w.r.t. {A}< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
Gd = linearize(mdl, io, options);
Gd.InputName = {< span class = "org-string" > 'Fex'< / span > , < span class = "org-string" > 'Fey'< / span > , < span class = "org-string" > 'Fez'< / span > , < span class = "org-string" > 'Mex'< / span > , < span class = "org-string" > 'Mey'< / span > , < span class = "org-string" > 'Mez'< / span > };
Gd.OutputName = {< span class = "org-string" > 'Edx'< / span > , < span class = "org-string" > 'Edy'< / span > , < span class = "org-string" > 'Edz'< / span > , < span class = "org-string" > 'Erx'< / span > , < span class = "org-string" > 'Ery'< / span > , < span class = "org-string" > 'Erz'< / span > };
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< / pre >
< / div >
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< p >
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The comparison of the two transfer functions is shown in Figure < a href = "#org2de43b3" > 1< / a > .
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< / p >
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< div id = "org2de43b3" class = "figure" >
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< p > < img src = "figs/comparison_Fext_F_fixed_base.png" alt = "comparison_Fext_F_fixed_base.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Comparison of the transfer functions from \(\bm{\mathcal{F}}\) to \(\mathcal{\bm{X}}\) and from \(\bm{\mathcal{F}}_{\text{ext}}\) to \(\mathcal{\bm{X}}\) (< a href = "./figs/comparison_Fext_F_fixed_base.png" > png< / a > , < a href = "./figs/comparison_Fext_F_fixed_base.pdf" > pdf< / a > )< / p >
< / div >
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< p >
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This can be understood from figure < a href = "#orgd6db375" > 2< / a > where \(\mathcal{F}_{x}\) and \(\mathcal{F}_{x,\text{ext}}\) have clearly the same effect on \(\mathcal{X}_{x}\).
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< / p >
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< div id = "orgd6db375" class = "figure" >
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< p > < img src = "figs/1dof_actuator_external_forces.png" alt = "1dof_actuator_external_forces.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Schematic representation of the stewart platform on a rigid support< / p >
< / div >
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< / div >
< / div >
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< div id = "outline-container-orgefde538" class = "outline-3" >
< h3 id = "orgefde538" > < span class = "section-number-3" > 1.2< / span > Comparison with a flexible support< / h3 >
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< div class = "outline-text-3" id = "text-1-2" >
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< p >
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We now add a flexible support under the Stewart platform.
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > ground = initializeGround(< span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'flexible'< / span > );
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< / pre >
< / div >
< p >
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And we perform again the identification.
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Controller'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Actuator Force Inputs [N]< / span >
io(io_i) = linio([mdl, < span class = "org-string" > '/Relative Motion Sensor'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Position/Orientation of {B} w.r.t. {A}< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize(mdl, io, options);
G.InputName = {< span class = "org-string" > 'F1'< / span > , < span class = "org-string" > 'F2'< / span > , < span class = "org-string" > 'F3'< / span > , < span class = "org-string" > 'F4'< / span > , < span class = "org-string" > 'F5'< / span > , < span class = "org-string" > 'F6'< / span > };
G.OutputName = {< span class = "org-string" > 'Edx'< / span > , < span class = "org-string" > 'Edy'< / span > , < span class = "org-string" > 'Edz'< / span > , < span class = "org-string" > 'Erx'< / span > , < span class = "org-string" > 'Ery'< / span > , < span class = "org-string" > 'Erz'< / span > };
Gc = minreal(G< span class = "org-type" > *< / span > inv(stewart.kinematics.J< span class = "org-type" > '< / span > ));
Gc.InputName = {< span class = "org-string" > 'Fnx'< / span > , < span class = "org-string" > 'Fny'< / span > , < span class = "org-string" > 'Fnz'< / span > , < span class = "org-string" > 'Mnx'< / span > , < span class = "org-string" > 'Mny'< / span > , < span class = "org-string" > 'Mnz'< / span > };
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Disturbances'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > , [], < span class = "org-string" > 'F_ext'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % External forces/torques applied on {B}< / span >
io(io_i) = linio([mdl, < span class = "org-string" > '/Relative Motion Sensor'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Position/Orientation of {B} w.r.t. {A}< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
Gd = linearize(mdl, io, options);
Gd.InputName = {< span class = "org-string" > 'Fex'< / span > , < span class = "org-string" > 'Fey'< / span > , < span class = "org-string" > 'Fez'< / span > , < span class = "org-string" > 'Mex'< / span > , < span class = "org-string" > 'Mey'< / span > , < span class = "org-string" > 'Mez'< / span > };
Gd.OutputName = {< span class = "org-string" > 'Edx'< / span > , < span class = "org-string" > 'Edy'< / span > , < span class = "org-string" > 'Edz'< / span > , < span class = "org-string" > 'Erx'< / span > , < span class = "org-string" > 'Ery'< / span > , < span class = "org-string" > 'Erz'< / span > };
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< / pre >
< / div >
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< p >
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The comparison between the obtained transfer functions is shown in Figure < a href = "#org593368e" > 3< / a > .
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< / p >
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< div id = "org593368e" class = "figure" >
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< p > < img src = "figs/comparison_Fext_F_flexible_base.png" alt = "comparison_Fext_F_flexible_base.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 3: < / span > Comparison of the transfer functions from \(\bm{\mathcal{F}}\) to \(\mathcal{\bm{X}}\) and from \(\bm{\mathcal{F}}_{\text{ext}}\) to \(\mathcal{\bm{X}}\) (< a href = "./figs/comparison_Fext_F_flexible_base.png" > png< / a > , < a href = "./figs/comparison_Fext_F_flexible_base.pdf" > pdf< / a > )< / p >
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< / div >
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< p >
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The addition of a flexible support can be schematically represented in Figure < a href = "#orga537ded" > 4< / a > .
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We see that \(\mathcal{F}_{x}\) applies a force both on \(m\) and \(m^{\prime}\) whereas \(\mathcal{F}_{x,\text{ext}}\) only applies a force on \(m\).
And thus \(\mathcal{F}_{x}\) and \(\mathcal{F}_{x,\text{ext}}\) have clearly < b > not< / b > the same effect on \(\mathcal{X}_{x}\).
< / p >
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< div id = "orga537ded" class = "figure" >
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< p > < img src = "figs/2dof_actuator_external_forces.png" alt = "2dof_actuator_external_forces.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Schematic representation of the stewart platform on top of a flexible support< / p >
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< / div >
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< / div >
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< / div >
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< div id = "outline-container-org53765b8" class = "outline-3" >
< h3 id = "org53765b8" > < span class = "section-number-3" > 1.3< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-1-3" >
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< div class = "important" id = "org35e4b5f" >
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< p >
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The transfer function from forces/torques applied by the actuators on the payload \(\bm{\mathcal{F}} = \bm{J}^T \bm{\tau}\) to the pose of the mobile platform \(\bm{\mathcal{X}}\) is the same as the transfer function from external forces/torques to \(\bm{\mathcal{X}}\) as long as the Stewart platform’ s base is fixed.
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< / p >
< / div >
< / div >
< / div >
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< / div >
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< div id = "outline-container-orgb6a1ef7" class = "outline-2" >
< h2 id = "orgb6a1ef7" > < span class = "section-number-2" > 2< / span > Comparison of the static transfer function and the Compliance matrix< / h2 >
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< div class = "outline-text-2" id = "text-2" >
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< p >
In this section, we see how the Compliance matrix of the Stewart platform is linked to the static relation between \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\).
< / p >
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< / div >
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< div id = "outline-container-org3f1c253" class = "outline-3" >
< h3 id = "org3f1c253" > < span class = "section-number-3" > 2.1< / span > Analysis< / h3 >
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< div class = "outline-text-3" id = "text-2-1" >
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< p >
Initialization of the Stewart platform.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, < span class = "org-string" > 'H'< / span > , 90e< span class = "org-type" > -< / span > 3, < span class = "org-string" > 'MO_B'< / span > , 45e< span class = "org-type" > -< / span > 3);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
stewart = initializeJointDynamics(stewart, < span class = "org-string" > 'type_F'< / span > , < span class = "org-string" > 'universal_p'< / span > , < span class = "org-string" > 'type_M'< / span > , < span class = "org-string" > 'spherical_p'< / span > );
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
stewart = initializeInertialSensor(stewart, < span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'none'< / span > );
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< / pre >
< / div >
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< p >
No flexibility below the Stewart platform and no payload.
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > ground = initializeGround(< span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'none'< / span > );
payload = initializePayload(< span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'none'< / span > );
controller = initializeController(< span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'open-loop'< / span > );
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< / pre >
< / div >
< p >
Estimation of the transfer function from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\):
< / p >
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< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Options for Linearized< / span > < / span >
options = linearizeOptions;
options.SampleTime = 0;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
mdl = < span class = "org-string" > 'stewart_platform_model'< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Controller'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Actuator Force Inputs [N]< / span >
io(io_i) = linio([mdl, < span class = "org-string" > '/Relative Motion Sensor'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Position/Orientation of {B} w.r.t. {A}< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize(mdl, io, options);
G.InputName = {< span class = "org-string" > 'F1'< / span > , < span class = "org-string" > 'F2'< / span > , < span class = "org-string" > 'F3'< / span > , < span class = "org-string" > 'F4'< / span > , < span class = "org-string" > 'F5'< / span > , < span class = "org-string" > 'F6'< / span > };
G.OutputName = {< span class = "org-string" > 'Edx'< / span > , < span class = "org-string" > 'Edy'< / span > , < span class = "org-string" > 'Edz'< / span > , < span class = "org-string" > 'Erx'< / span > , < span class = "org-string" > 'Ery'< / span > , < span class = "org-string" > 'Erz'< / span > };
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< / pre >
< / div >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > Gc = minreal(G< span class = "org-type" > *< / span > inv(stewart.kinematics.J< span class = "org-type" > '< / span > ));
Gc.InputName = {< span class = "org-string" > 'Fnx'< / span > , < span class = "org-string" > 'Fny'< / span > , < span class = "org-string" > 'Fnz'< / span > , < span class = "org-string" > 'Mnx'< / span > , < span class = "org-string" > 'Mny'< / span > , < span class = "org-string" > 'Mnz'< / span > };
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< / pre >
< / div >
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< p >
Let’ s first look at the low frequency transfer function matrix from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\).
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-right" / >
< col class = "org-right" / >
< col class = "org-right" / >
< col class = "org-right" / >
< col class = "org-right" / >
< / colgroup >
< tbody >
< tr >
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< td class = "org-right" > 4.7e-08< / td >
< td class = "org-right" > -7.2e-19< / td >
< td class = "org-right" > 5.0e-18< / td >
< td class = "org-right" > -8.9e-18< / td >
< td class = "org-right" > 3.2e-07< / td >
< td class = "org-right" > 9.9e-18< / td >
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< / tr >
< tr >
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< td class = "org-right" > 4.7e-18< / td >
< td class = "org-right" > 4.7e-08< / td >
< td class = "org-right" > -5.7e-18< / td >
< td class = "org-right" > -3.2e-07< / td >
< td class = "org-right" > -1.6e-17< / td >
< td class = "org-right" > -1.7e-17< / td >
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< / tr >
< tr >
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< td class = "org-right" > 3.3e-18< / td >
< td class = "org-right" > -6.3e-18< / td >
< td class = "org-right" > 2.1e-08< / td >
< td class = "org-right" > 4.4e-17< / td >
< td class = "org-right" > 6.6e-18< / td >
< td class = "org-right" > 7.4e-18< / td >
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< / tr >
< tr >
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< td class = "org-right" > -3.2e-17< / td >
< td class = "org-right" > -3.2e-07< / td >
< td class = "org-right" > 6.2e-18< / td >
< td class = "org-right" > 5.2e-06< / td >
< td class = "org-right" > -3.5e-16< / td >
< td class = "org-right" > 6.3e-17< / td >
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< / tr >
< tr >
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< td class = "org-right" > 3.2e-07< / td >
< td class = "org-right" > 2.7e-17< / td >
< td class = "org-right" > 4.8e-17< / td >
< td class = "org-right" > -4.5e-16< / td >
< td class = "org-right" > 5.2e-06< / td >
< td class = "org-right" > -1.2e-19< / td >
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< / tr >
< tr >
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< td class = "org-right" > 4.0e-17< / td >
< td class = "org-right" > -9.5e-17< / td >
< td class = "org-right" > 8.4e-18< / td >
< td class = "org-right" > 4.3e-16< / td >
< td class = "org-right" > 5.8e-16< / td >
< td class = "org-right" > 1.7e-06< / td >
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< / tr >
< / tbody >
< / table >
< p >
And now at the Compliance matrix.
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-right" / >
< col class = "org-right" / >
< col class = "org-right" / >
< col class = "org-right" / >
< col class = "org-right" / >
< / colgroup >
< tbody >
< tr >
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< td class = "org-right" > 4.7e-08< / td >
< td class = "org-right" > -2.0e-24< / td >
< td class = "org-right" > 7.4e-25< / td >
< td class = "org-right" > 5.9e-23< / td >
< td class = "org-right" > 3.2e-07< / td >
< td class = "org-right" > 5.9e-24< / td >
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< / tr >
< tr >
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< td class = "org-right" > -7.1e-25< / td >
< td class = "org-right" > 4.7e-08< / td >
< td class = "org-right" > 2.9e-25< / td >
< td class = "org-right" > -3.2e-07< / td >
< td class = "org-right" > -5.4e-24< / td >
< td class = "org-right" > -3.3e-23< / td >
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< / tr >
< tr >
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< td class = "org-right" > 7.9e-26< / td >
< td class = "org-right" > -6.4e-25< / td >
< td class = "org-right" > 2.1e-08< / td >
< td class = "org-right" > 1.9e-23< / td >
< td class = "org-right" > 5.3e-25< / td >
< td class = "org-right" > -6.5e-40< / td >
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< / tr >
< tr >
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< td class = "org-right" > 1.4e-23< / td >
< td class = "org-right" > -3.2e-07< / td >
< td class = "org-right" > 1.3e-23< / td >
< td class = "org-right" > 5.2e-06< / td >
< td class = "org-right" > 4.9e-22< / td >
< td class = "org-right" > -3.8e-24< / td >
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< / tr >
< tr >
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< td class = "org-right" > 3.2e-07< / td >
< td class = "org-right" > 7.6e-24< / td >
< td class = "org-right" > 1.2e-23< / td >
< td class = "org-right" > 6.9e-22< / td >
< td class = "org-right" > 5.2e-06< / td >
< td class = "org-right" > -2.6e-22< / td >
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< / tr >
< tr >
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< td class = "org-right" > 7.3e-24< / td >
< td class = "org-right" > -3.2e-23< / td >
< td class = "org-right" > -1.6e-39< / td >
< td class = "org-right" > 9.9e-23< / td >
< td class = "org-right" > -3.3e-22< / td >
< td class = "org-right" > 1.7e-06< / td >
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< / tr >
< / tbody >
< / table >
< / div >
< / div >
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< div id = "outline-container-orga9eb2fd" class = "outline-3" >
< h3 id = "orga9eb2fd" > < span class = "section-number-3" > 2.2< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-2-2" >
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< div class = "important" id = "orgcecc007" >
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< p >
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The low frequency transfer function matrix from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\) corresponds to the compliance matrix of the Stewart platform.
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< / p >
< / div >
< / div >
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2021-01-08 ven. 15:30< / p >
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< / body >
< / html >
