diff --git a/docs/cubic-configuration.html b/docs/cubic-configuration.html index b9d11cc..b07d07c 100644 --- a/docs/cubic-configuration.html +++ b/docs/cubic-configuration.html @@ -4,7 +4,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
- +generateCubicConfiguration
: Generate a Cubic Configuration
+generateCubicConfiguration
: Generate a Cubic Configuration
-To generate and study the Cubic configuration, generateCubicConfiguration
is used (description in section 2.1).
+To generate and study the Cubic configuration, generateCubicConfiguration
is used (description in section 3.1).
The goal is to study the benefits of using a cubic configuration:
+We here study the effect of the size of the cube used for the Stewart Cubic configuration. +
+ ++We fix the height of the Stewart platform, the center of the cube is at the center of the Stewart platform and the frames \(\{A\}\) and \(\{B\}\) are also taken at the center of the cube. +
+ ++We only vary the size of the cube. +
+ +Hcs = 1e-3*[250:20:350]; % Heights for the Cube [m] +Ks = zeros(6, 6, length(Hcs)); ++
+The height of the Stewart platform is fixed: +
+H = 100e-3; % height of the Stewart platform [m] ++
+The frames \(\{A\}\) and \(\{B\}\) are positioned at the Stewart platform center as well as the cube’s center: +
+MO_B = -50e-3; % Position {B} with respect to {M} [m] +FOc = H + MO_B; % Center of the cube with respect to {F} ++
stewart = initializeStewartPlatform(); +stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B); +for i = 1:length(Hcs) + Hc = Hcs(i); + stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 0, 'MHb', 0); + stewart = computeJointsPose(stewart); + stewart = initializeStrutDynamics(stewart, 'K', ones(6,1)); + stewart = computeJacobian(stewart); + Ks(:,:,i) = stewart.kinematics.K; +end ++
+We find that for all the cube’s size, \(k_x = k_y = k_z = k\) where \(k\) is the strut stiffness. +We also find that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) are varying with the cube’s size (figure 9). +
+ +figure; +hold on; +plot(Hcs, squeeze(Ks(4, 4, :)), 'DisplayName', '$k_{\theta_x} = k_{\theta_y}$'); +plot(Hcs, squeeze(Ks(6, 6, :)), 'DisplayName', '$k_{\theta_z}$'); +hold off; +legend('location', 'northwest'); +xlabel('Cube Size [m]'); ylabel('Rotational stiffnes [normalized]'); ++
+
+Figure 9: \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) function of the size of the cube
++We observe that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) increase linearly with the cube size. +
+ ++In order to maximize the rotational stiffness of the Stewart platform, the size of the cube should be the highest possible. +
+ +generateCubicConfiguration
: Generate a Cubic ConfigurationgenerateCubicConfiguration
: Generate a Cubic Configuration-
Figure 9: Cubic Configuration
+Figure 10: Cubic Configuration
Created: 2020-02-12 mer. 10:22
+Created: 2020-02-12 mer. 10:37