class SignConventions "Sign Conventions"
extends Modelica.Icons.Information;
annotation (
DocumentationClass = true,
Documentation(info = "<html>\n\n<p>\nThe variables of a component of this library can be accessed in the\nusual way. However, since most of these variables are basically elements\nof <strong>vectors</strong>, i.e., have a direction, the question arises how the\nsigns of variables shall be interpreted. The basic idea is explained\nat hand of the following figure:\n</p>\n\n<p>\n<img src=\"modelica://Modelica/Resources/Images/Mechanics/Rotational/drive2.png\" alt=\"drive2\">\n</p>\n\n<p>\nIn the figure, three identical drive trains are shown. The only\ndifference is that the gear of the middle drive train and the\ngear as well as the right inertia of the lower drive train\nare horizontally flipped with regards to the upper drive train.\nThe signs of variables are now interpreted in the following way:\nDue to the 1-dimensional nature of the model, all components are\nbasically connected together along one line (more complicated\ncases are discussed below). First, one has to define\na <strong>positive</strong> direction of this line, called <strong>axis of rotation</strong>.\nIn the top part of the figure this is characterized by an arrow\ndefined as <code>axis of rotation</code>. The simple rule is now:\nIf a variable of a component is positive and can be interpreted as\nthe element of a vector (e.g., torque or angular velocity vector), the\ncorresponding vector is directed into the positive direction\nof the axis of rotation. In the following figure, the right-most\ninertias of the figure above are displayed with the positive\nvector direction displayed according to this rule:\n</p>\n\n<p>\n<img src=\"modelica://Modelica/Resources/Images/Mechanics/Rotational/drive3.png\" alt=\"drive3\">\n</p>\n<p>\nThe cut-torques <code>J2.flange_a.tau, J4.flange_a.tau, J6.flange_b.tau</code>\nof the right inertias are all identical and are directed into the\ndirection of rotation if the values are positive. Similarly,\nthe angular velocities <code>J2.w, J4.w, J6.w</code> of the right inertias\nare all identical and are also directed into the\ndirection of rotation if the values are positive. Some special\ncases are shown in the next figure:\n</p>\n\n<p>\n<img src=\"modelica://Modelica/Resources/Images/Mechanics/Rotational/drive4.png\" alt=\"drive4\">\n</p>\n\n<p>\nIn the upper part of the figure, two variants of the connection of an\nexternal torque and an inertia are shown. In both cases, a positive\nsignal input into the torque component accelerates the inertias\n<code>inertia1, inertia2</code> into the positive axis of rotation,\ni.e., the angular accelerations <code>inertia1.a, inertia2.a</code>\nare positive and are directed along the \"axis of rotation\" arrow.\nIn the lower part of the figure the connection of inertias with\na planetary gear is shown. Note, that the three flanges of the\nplanetary gearbox are located along the axis of rotation and that\nthe axis direction determines the positive rotation along these\nflanges. As a result, the positive rotation for <code>inertia4, inertia6</code>\nis as indicated with the additional grey arrows.\n</p>\n</html>"));
end SignConventions;