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Nano-Hexapod

+
+

Table of Contents

+
+ +
+
+ +
+

1 Nano-Hexapod

+
+
+
+

1.1 Nano Hexapod object

+
+

+The nano-hexapod can be initialized and configured using the initializeNanoHexapodFinal function. +

+ +
+
n_hexapod = initializeNanoHexapodFinal('flex_bot_type', '4dof', ...
+                                       'flex_top_type', '3dof', ...
+                                       'motion_sensor_type', 'struts', ...
+                                       'actuator_type', '2dof');
+
+
+
+
+ +
+

1.2 Jacobian from Solidworks Model

+
+

+Center of joints a_i with respect to {F}: +

+
+
Fa = [[-86.05,  -74.78, 22.49],
+      [86.05,   -74.78, 22.49],
+      [107.79,  -37.13, 22.49],
+      [21.74,   111.91, 22.49],
+      [-21.74,  111.91, 22.49],
+      [-107.79, -37.13, 22.49]]'*1e-3;
+
+
+ +

+Center of joints a_i with respect to {M}: +

+
+
Mb = [[-28.47, -106.25, -22.50],
+      [28.47,  -106.25, -22.50],
+      [106.25,  28.47,  -22.50],
+      [77.78,   77.78,  -22.50],
+      [-77.78,  77.78,  -22.50],
+      [-106.25, 28.47,  -22.50]]'*1e-3;
+
+
+ +
+
Fb = Mb + [0; 0; 95e-3];
+
+si = Fb - Fa;
+si = si./vecnorm(si);
+
+
+ +
+
ki = ones(1,6);
+bi = Fb;
+
+
+ +
+
ki.*si*si'
+
+
+ + + + +++ ++ ++ + + + + + + + + + + + + + + + + + + + +
1.89772.4659e-171.3383e-18
2.4659e-171.8977-2.3143e-05
1.3383e-18-2.3143e-052.2046
+ +
+
OkX = (ki.*cross(bi, si)*si')/(ki.*si*si');
+Ok = [OkX(3,2);OkX(1,3);OkX(2,1)]
+
+
+ + + + +++ + + + + + + + + + + + + + +
-1.7444e-18
2.1511e-06
0.052707
+ +

+The center of the cube is therefore 52.7mm above the bottom platform {F} frame. +

+ +

+Let’s compute the Jacobian at this location: +

+
+
Jk = [si', cross(bi - Ok, si)'];
+
+
+ +

+And the stiffness matrix: +

+
+
Jk'*diag(ki)*Jk
+
+
+ + + + +++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
1.8977000-3.4694e-182.5509e-06
01.8977-2.3143e-054.1751e-061.3878e-170
0-2.3143e-052.2046-5.0916e-11-3.4694e-180
04.1751e-06-5.0916e-110.0125942.1684e-198.6736e-19
-3.2704e-180-4.206e-183.9451e-190.012594-9.3183e-08
2.5509e-06008.6736e-19-9.3183e-080.043362
+
+
+ +
+

1.3 Jacobian for encoders on the plates

+
+

+Goal: Compute the 6-DoF motion of the top platform (relative to the bottom platform) from the 6 encoder measurements. +

+ +

+The main differences with the case where the encoders are parallel with the strut are: +

+
    +
  • the encoder and ruler may not be parallel anymore as the top platform is moving
    • +
  • the derivation of the Jacobian (if possible) will not be the same
    • +
+
+
+ +
+

1.4 Compare encoders on the struts and encoders on the platforms

+
+
+
%% Options for Linearized
+options = linearizeOptions;
+options.SampleTime = 0;
+
+%% Name of the Simulink File
+mdl = 'nano_hexapod';
+
+%% Input/Output definition
+clear io; io_i = 1;
+io(io_i) = linio([mdl, '/F'],  1, 'openinput');  io_i = io_i + 1; % Actuator Inputs
+io(io_i) = linio([mdl, '/D'],  1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs
+
+
+ +
+
n_hexapod.motion_sensor = struct();
+n_hexapod.motion_sensor.type = 1; % 1: Leg / 2: Plate
+
+
+ +
+
Gs = linearize(mdl, io, 0.0, options);
+Gs.InputName  = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
+Gs.OutputName = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'};
+
+
+ +
+
n_hexapod.motion_sensor = struct();
+n_hexapod.motion_sensor.type = 2; % 1: Leg / 2: Plate
+
+
+ +
+
Gp = linearize(mdl, io, 0.0, options);
+Gp.InputName  = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
+Gp.OutputName = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'};
+
+
+
+
+ +
+

1.5 Nano Hexapod

+
+
+
%% Options for Linearized
+options = linearizeOptions;
+options.SampleTime = 0;
+
+%% Name of the Simulink File
+mdl = 'nano_hexapod';
+
+%% Input/Output definition
+clear io; io_i = 1;
+io(io_i) = linio([mdl, '/F'],  1, 'openinput');  io_i = io_i + 1; % Actuator Inputs
+io(io_i) = linio([mdl, '/Fe'], 1, 'openinput');  io_i = io_i + 1; % External Force
+io(io_i) = linio([mdl, '/D'],  1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs
+io(io_i) = linio([mdl, '/Fm'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensors
+io(io_i) = linio([mdl, '/X'],  1, 'openoutput'); io_i = io_i + 1; % Absolute Motion of top platform
+
+%% Run the linearization
+G = linearize(mdl, io, 0.0, options);
+G.InputName  = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6', ...
+                'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
+G.OutputName = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6', ...
+                'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6' ...
+                'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
+
+
+ +
+size(G)
+State-space model with 18 outputs, 12 inputs, and 60 states.
+
+ + +

+Verify the number of DOF: +

+ + + +++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
ElementDoF
Bot Plate0
Struts6*4
Top Plate + Sample12
Total:36
+
+ +
+

1.5.1 DVF Plant

+
+

+The DC gain from actuator to relative motion sensor should be equal to (for the 2dof APA): +\[ \frac{1}{k + k_a + kk_a/k_e} \] +

+ +
+1.8732e-08
+
+ + +

+Which is almost the case: +

+ + + + +++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
-1.8676e-085.2396e-11-8.8935e-112.6392e-119.7629e-11-1.5609e-10
-1.4754e-11-1.8725e-081.4348e-11-5.7189e-11-3.3327e-117.0799e-11
-3.4924e-11-7.7445e-11-1.8607e-08-4.6578e-11-1.9592e-114.0299e-11
6.1699e-11-7.1962e-111.3374e-11-1.8623e-08-1.7898e-105.4541e-11
9.735e-11-1.0698e-10-1.6424e-112.3718e-11-1.8826e-088.387e-11
-3.94e-112.6436e-11-1.1338e-105.0793e-111.2358e-10-1.8792e-08
+ +

+Other (off-diagonal) elements should be close to zero (probably limited to joint’s stiffness). +However, when setting joint’s axial stiffness to infinity, I obtain better diagonal. +

+ + +
+

nano_hexapod_struts_2dof_dvf_plant.png +

+

Figure 1: IFF Plant

+
+
+
+ +
+

1.5.2 IFF Plant

+
+ +
+

nano_hexapod_struts_2dof_iff_plant.png +

+

Figure 2: DVF Plant

+
+
+
+
+ +
+

1.6 Decoupling at the CoK

+
+
+
Gx = inv(Jk)*G({'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})*inv(Jk');
+Gx.inputname  = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
+Gx.outputname = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
+
+
+ + + + +++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
-9.8399e-09-8.0785e-11-1.5723e-112.6356e-10-4.9857e-105.2177e-11
-8.7554e-11-9.8585e-092.6292e-112.0485e-102.0385e-108.2942e-11
4.3837e-11-5.5862e-14-8.4859e-09-9.0036e-122.9325e-10-3.104e-11
1.901e-095.3078e-10-7.5477e-10-1.4759e-06-7.7918e-09-7.491e-10
-7.1795e-11-1.6333e-09-1.8359e-105.2707e-09-1.4794e-063.2304e-10
7.0322e-111.7713e-12-5.8019e-117.4838e-11-8.9677e-10-4.2938e-07
+
+
+ +
+

1.7 Jacobian

+
+
+
+

1.7.1 Compute Jacobian

+
+
+
Ai = [out.b1.Data(1,:)
+      out.b2.Data(1,:)
+      out.b3.Data(1,:)
+      out.b4.Data(1,:)
+      out.b5.Data(1,:)
+      out.b6.Data(1,:)]';
+
+
+Bi = [out.a1.Data(1,:)
+      out.a2.Data(1,:)
+      out.a3.Data(1,:)
+      out.a4.Data(1,:)
+      out.a5.Data(1,:)
+      out.a6.Data(1,:)]';
+
+
+ +
+
stewart = initializeStewartPlatform();
+stewart = initializeFramesPositions(stewart, 'H', 95e-3, 'MO_B', 150e-3);
+stewart = generateGeneralConfiguration(stewart);
+stewart.platform_F.Fa = Ai;
+stewart.platform_M.Mb = Bi - [0;0;1]*stewart.geometry.H;
+stewart = computeJointsPose(stewart);
+stewart = initializeStewartPose(stewart, 'AP', [0;0;0], 'ARB', eye(3));
+
+
+ +
+
stewart = initializeCylindricalPlatforms(stewart);
+stewart = initializeCylindricalStruts(stewart);
+
+
+ +
+
stewart = initializeStrutDynamics(stewart, 'K', 1e6*ones(6,1), 'C', 1e2*ones(6,1));
+stewart = initializeAmplifiedStrutDynamics(stewart);
+stewart = initializeJointDynamics(stewart);
+
+
+ +
+
displayArchitecture(stewart, 'views', 'all');
+
+
+ +
+describeStewartPlatform(stewart)
+GEOMETRY:
+- The height between the fixed based and the top platform is 95 [mm].
+- Frame {A} is located 150 [mm] above the top platform.
+- The initial length of the struts are:
+	 82.8, 82.8, 82.8, 82.8, 82.8, 82.8 [mm]
+
+ACTUATORS:
+- The actuators are mechanicaly amplified.
+- The vertical stiffness and damping contribution of the piezoelectric stack is:
+	 ka = 2e+07 [N/m] 	 ca = 1e+01 [N/(m/s)]
+- Vertical stiffness when the piezoelectric stack is removed is:
+	 kr = 5e+06 [N/m] 	 cr = 1e+01 [N/(m/s)]
+
+JOINTS:
+- The joints on the fixed based are universal joints
+- The joints on the mobile based are spherical joints
+- The position of the joints on the fixed based with respect to {F} are (in [mm]):
+	 -86.2 	 -74.7 	  22.3
+	  86.3 	 -74.6 	  22.3
+	  108 	 -37.3 	  22.3
+	  21.5 	  112 	  22.3
+	 -21.5 	  112 	  22.3
+	 -108 	 -37.5 	  22.2
+- The position of the joints on the mobile based with respect to {M} are (in [mm]):
+	 -28.4 	 -106 	 -22.4
+	  28.5 	 -106 	 -22.5
+	  106 	  28.5 	 -22.5
+	  77.8 	  77.8 	 -22.5
+	 -77.8 	  77.8 	 -22.5
+	 -106 	  28.4 	 -22.5
+
+ +
+
stewart = computeJacobian(stewart);
+
+
+
+
+ +
+

1.7.2 Verify Jacobian

+
+
+
load('./mat/nano_hexapod_object.mat', 'stewart');
+J = stewart.kinematics.J;
+
+
+ +

+Transformation of motion: +

+
+
G1 = -inv(J)*G({'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'});
+G2 = G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'});
+
+
+ +

+Transformation of Forces and Torques +

+
+
G1 = G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'});
+G2 = G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})*inv(J');
+
+
+ +

+Not working because the forces applied on the APA are not really forces applied on the top platform (reduced by a factor ~ka/ke) +

+
+
+ +
+

1.7.3 Plant from APA forces to sample’s displacement

+
+
+
Gx = G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})*inv(J');
+Gx.inputname  = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
+
+
+
+
+ +
+

1.7.4 Plant in the Cartesian frame

+
+

+Transfer function from forces/torque to displacement/rotation: +

+
+
GJ = inv(J)*G({'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})*inv(J');
+GJ.inputname  = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
+GJ.outputname = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
+
+
+
+
+ +
+

1.7.5 Plant in the frame of the legs => Verification of Jacobian for displacements

+
+

+Transfer Function in the frame of the legs +

+
+
G1 = -J*G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'});
+G1.outputname = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'};
+
+G2 = G({'D1', 'D2', 'D3', 'D4', 'D5', 'D6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'});
+
+
+ +
+

+It is working fine (until internal resonance of strut). +

+ +
+
+
+
+ +
+

1.8 Stiffness matrix

+
+

+Neglecting stiffness of the joints, we have: +\[ K = J^t \mathcal{K} J \] +where \(\mathcal{K}\) is a diagonal 6x6 matrix with axial stiffness of the struts on the diagonal. +

+ +

+Let’s note the axial stiffness of the APA: +\[ k_{\text{APA}} = k + \frac{k_e k_a}{k_e + k_a} \] +

+ +

+Them axial stiffness of the struts \(k_s\): +\[ k_s = \frac{k_z k_{\text{APA}}}{k_z + 2 k_{\text{APA}}} \] +

+ +
+
kAPA = k + ke*ka/(ke + ka);
+ks = kz*kAPA/(kz + 2*kAPA);
+
+
+ +
+
Ks = J'*(ks*eye(6))*J
+
+
+ + + + +++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
1.9937e-067.7027e-12-1.5885e-11-1.6811e-108.7902e-063.0476e-11
7.7027e-121.9937e-062.7221e-11-8.7901e-066.5081e-122.8619e-11
-1.5885e-112.7221e-112.6114e-07-1.3209e-10-6.1725e-114.0402e-11
-1.6811e-10-8.7901e-06-1.3209e-104.5712e-05-5.7781e-10-4.5817e-10
8.7902e-066.5081e-12-6.1725e-11-5.7781e-104.5712e-055.1628e-10
3.0476e-112.8619e-114.0402e-11-4.5817e-105.1628e-101.3277e-05
+ + + + +++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
1.9869e-062.043e-081.6444e-09-4.094e-088.7579e-06-3.5002e-09
3.746e-091.9841e-06-5.5274e-09-8.7257e-06-5.5082e-08-7.6978e-09
-3.2056e-09-6.4295e-112.6079e-073.4103e-10-9.3873e-099.6146e-10
-1.1677e-08-8.736e-062.4322e-084.5343e-052.52e-072.5932e-08
8.7439e-068.441e-085.9144e-09-1.6879e-074.546e-05-9.8986e-09
3.3453e-094.508e-101.8718e-09-2.7294e-092.8776e-081.3193e-05
+ +

+We can see that we have almost the same stiffness: +

+ + + + +++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
1.00340.00037703-0.00965970.00410631.0037-0.0087071
0.00205621.0048-0.00492471.0074-0.00011815-0.0037178
0.0049552-0.423381.0013-0.387340.00657540.042021
0.0143971.0062-0.0054311.0081-0.0022929-0.017668
1.00537.7101e-05-0.0104360.00342331.0055-0.052157
0.00911020.0634850.0215840.167860.0179411.0063
+
+
+
+ +
+

2 Function - Initialize Nano Hexapod

+
+

+ +

+
+ +
+

Function description

+
+
+
  function [nano_hexapod] = initializeNanoHexapodFinal(args)
+
+
+
+
+ +
+

Optional Parameters

+
+
+
  arguments
+      %% Bottom Flexible Joints
+      args.flex_bot_type      char {mustBeMember(args.flex_bot_type,{'2dof', '3dof', '4dof', 'flexible'})} = '4dof'
+      args.flex_bot_kRx (6,1) double {mustBeNumeric} = ones(6,1)*5 % X bending stiffness [Nm/rad]
+      args.flex_bot_kRy (6,1) double {mustBeNumeric} = ones(6,1)*5 % Y bending stiffness [Nm/rad]
+      args.flex_bot_kRz (6,1) double {mustBeNumeric} = ones(6,1)*260 % Torsionnal stiffness [Nm/rad]
+      args.flex_bot_kz  (6,1) double {mustBeNumeric} = ones(6,1)*1e8 % Axial Stiffness [N/m]
+      args.flex_bot_cRx (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % X bending Damping [Nm/(rad/s)]
+      args.flex_bot_cRy (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % Y bending Damping [Nm/(rad/s)]
+      args.flex_bot_cRz (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % Torsionnal Damping [Nm/(rad/s)]
+      args.flex_bot_cz  (6,1) double {mustBeNumeric} = ones(6,1)*1e2 % Axial Damping [N/(m/s)]
+      %% Top Flexible Joints
+      args.flex_top_type      char {mustBeMember(args.flex_top_type,{'2dof', '3dof', '4dof', 'flexible'})} = '4dof'
+      args.flex_top_kRx (6,1) double {mustBeNumeric} = ones(6,1)*5 % X bending stiffness [Nm/rad]
+      args.flex_top_kRy (6,1) double {mustBeNumeric} = ones(6,1)*5 % Y bending stiffness [Nm/rad]
+      args.flex_top_kRz (6,1) double {mustBeNumeric} = ones(6,1)*260 % Torsionnal stiffness [Nm/rad]
+      args.flex_top_kz  (6,1) double {mustBeNumeric} = ones(6,1)*1e8 % Axial Stiffness [N/m]
+      args.flex_top_cRx (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % X bending Damping [Nm/(rad/s)]
+      args.flex_top_cRy (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % Y bending Damping [Nm/(rad/s)]
+      args.flex_top_cRz (6,1) double {mustBeNumeric} = ones(6,1)*0.1 % Torsionnal Damping [Nm/(rad/s)]
+      args.flex_top_cz  (6,1) double {mustBeNumeric} = ones(6,1)*1e2 % Axial Damping [N/(m/s)]
+      %% Relative Motion Sensor
+      args.motion_sensor_type char {mustBeMember(args.motion_sensor_type,{'struts', 'plates'})} = 'struts'
+      %% Actuators
+      args.actuator_type char {mustBeMember(args.actuator_type,{'2dof', 'flexible frame', 'flexible'})} = 'flexible'
+      args.actuator_Ga  (6,1) double {mustBeNumeric} = ones(6,1)*1 % Actuator gain [N/V]
+      args.actuator_Gs  (6,1) double {mustBeNumeric} = ones(6,1)*1 % Sensor gain [V/m]
+      % For 2DoF
+      args.actuator_k   (6,1) double {mustBeNumeric} = ones(6,1)*0.35e6 % [N/m]
+      args.actuator_ke  (6,1) double {mustBeNumeric} = ones(6,1)*1.5e6 % [N/m]
+      args.actuator_ka  (6,1) double {mustBeNumeric} = ones(6,1)*43e6 % [N/m]
+      args.actuator_c   (6,1) double {mustBeNumeric} = ones(6,1)*3e1 % [N/(m/s)]
+      args.actuator_ce  (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % [N/(m/s)]
+      args.actuator_ca  (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % [N/(m/s)]
+      args.actuator_Leq (6,1) double {mustBeNumeric} = ones(6,1)*0.056 % [m]
+      % For Flexible Frame
+      args.actuator_ks (6,1) double {mustBeNumeric} = ones(6,1)*235e6 % Stiffness of one stack [N/m]
+      args.actuator_cs (6,1) double {mustBeNumeric} = ones(6,1)*1e1 % Stiffness of one stack [N/m]
+      % For Flexible
+      args.actuator_xi  (1,1) double {mustBeNumeric} = 0.01 % Sensor gain [V/m]
+  end
+
+
+
+
+ +
+

Nano Hexapod Object

+
+
+
nano_hexapod = struct();
+
+
+
+
+ +
+

Flexible Joints - Bot

+
+
+
nano_hexapod.flex_bot = struct();
+
+switch args.flex_bot_type
+  case '2dof'
+    nano_hexapod.flex_bot.type = 1;
+  case '3dof'
+    nano_hexapod.flex_bot.type = 2;
+  case '4dof'
+    nano_hexapod.flex_bot.type = 3;
+  case 'flexible'
+    nano_hexapod.flex_bot.type = 4;
+end
+
+nano_hexapod.flex_bot.kRx = args.flex_bot_kRx; % X bending stiffness [Nm/rad]
+nano_hexapod.flex_bot.kRy = args.flex_bot_kRy; % Y bending stiffness [Nm/rad]
+nano_hexapod.flex_bot.kRz = args.flex_bot_kRz; % Torsionnal stiffness [Nm/rad]
+nano_hexapod.flex_bot.kz  = args.flex_bot_kz;  % Axial stiffness [N/m]
+
+nano_hexapod.flex_bot.cRx = args.flex_bot_cRx; % [Nm/(rad/s)]
+nano_hexapod.flex_bot.cRy = args.flex_bot_cRy; % [Nm/(rad/s)]
+nano_hexapod.flex_bot.cRz = args.flex_bot_cRz; % [Nm/(rad/s)]
+nano_hexapod.flex_bot.cz  = args.flex_bot_cz;  %[N/(m/s)]
+
+
+
+
+ +
+

Flexible Joints - Top

+
+
+
nano_hexapod.flex_top = struct();
+
+switch args.flex_top_type
+  case '2dof'
+    nano_hexapod.flex_top.type = 1;
+  case '3dof'
+    nano_hexapod.flex_top.type = 2;
+  case '4dof'
+    nano_hexapod.flex_top.type = 3;
+  case 'flexible'
+    nano_hexapod.flex_top.type = 4;
+end
+
+nano_hexapod.flex_top.kRx = args.flex_top_kRx; % X bending stiffness [Nm/rad]
+nano_hexapod.flex_top.kRy = args.flex_top_kRy; % Y bending stiffness [Nm/rad]
+nano_hexapod.flex_top.kRz = args.flex_top_kRz; % Torsionnal stiffness [Nm/rad]
+nano_hexapod.flex_top.kz  = args.flex_top_kz;  % Axial stiffness [N/m]
+
+nano_hexapod.flex_top.cRx = args.flex_top_cRx; % [Nm/(rad/s)]
+nano_hexapod.flex_top.cRy = args.flex_top_cRy; % [Nm/(rad/s)]
+nano_hexapod.flex_top.cRz = args.flex_top_cRz; % [Nm/(rad/s)]
+nano_hexapod.flex_top.cz  = args.flex_top_cz;  %[N/(m/s)]
+
+
+
+
+ +
+

Relative Motion Sensor

+
+
+
nano_hexapod.motion_sensor = struct();
+
+switch args.motion_sensor_type
+  case 'struts'
+    nano_hexapod.motion_sensor.type = 1;
+  case 'plates'
+    nano_hexapod.motion_sensor.type = 2;
+end
+
+
+
+
+ +
+

Amplified Piezoelectric Actuator

+
+
+
nano_hexapod.actuator = struct();
+
+switch args.actuator_type
+  case '2dof'
+    nano_hexapod.actuator.type = 1;
+  case 'flexible frame'
+    nano_hexapod.actuator.type = 2;
+  case 'flexible'
+    nano_hexapod.actuator.type = 3;
+end
+
+
+ +
+
nano_hexapod.actuator.Ga = args.actuator_Ga; % Actuator gain [N/V]
+nano_hexapod.actuator.Gs = args.actuator_Gs; % Sensor gain [V/m]
+
+
+ +

+2dof +

+
+
nano_hexapod.actuator.k  = args.actuator_k;  % [N/m]
+nano_hexapod.actuator.ke = args.actuator_ke; % [N/m]
+nano_hexapod.actuator.ka = args.actuator_ka; % [N/m]
+
+nano_hexapod.actuator.c  = args.actuator_c;  % [N/(m/s)]
+nano_hexapod.actuator.ce = args.actuator_ce; % [N/(m/s)]
+nano_hexapod.actuator.ca = args.actuator_ca; % [N/(m/s)]
+
+nano_hexapod.actuator.Leq = args.actuator_Leq; % [m]
+
+
+ +

+Flexible frame and fully flexible +

+
+
switch args.actuator_type
+  case 'flexible frame'
+    nano_hexapod.actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix
+    nano_hexapod.actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix
+    nano_hexapod.actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m]
+  case 'flexible'
+    nano_hexapod.actuator.K = readmatrix('APA300ML_full_mat_K.CSV'); % Stiffness Matrix
+    nano_hexapod.actuator.M = readmatrix('APA300ML_full_mat_M.CSV'); % Mass Matrix
+    nano_hexapod.actuator.P = extractNodes('APA300ML_full_out_nodes_3D.txt'); % Node coordiantes [m]
+end
+
+nano_hexapod.actuator.xi = args.actuator_xi; % Damping ratio
+
+nano_hexapod.actuator.ks = args.actuator_ks; % Stiffness of one stack [N/m]
+nano_hexapod.actuator.cs = args.actuator_cs; % Damping of one stack [N/m]
+
+
+
+
+ +
+

Save the Structure

+
+
+
if nargout == 0
+  save('./mat/stages.mat', 'nano_hexapod', '-append');
+end
+
+
+
+
+
+
+
+

Author: Dehaeze Thomas

+

Created: 2021-04-19 lun. 16:22

+
+ +