سورس شبیه سازی چرخ دنده در متلب

در  این پست قصد ارائه سورس حرکت دو چرخ دنده داخلی(Internal Gears) به زبان متلب را داریم. با استفاده از حرکت موس شما می توانید چاخ دنده را به حرکت درآوردید. این برنامه را می توانید با سه پارامتر اجرا نمایید؛ تعیین teeth، spokes و ratio که مقادری پیش فرض هر یک از آنها بصورت زیر می باشد:

GEAR3D(‘teeth’, 30) – default is 50.
GEAR3D(‘spokes’, 4) – default is 8.
GEAR3D(‘ratio’, 2) – default is 3. This also determines how big the ground radius is.

خروجی این برنامه بصورت زیر می باشد:

Internal Gears Simulation in MATLAB

سورس کامل این برنامه:

function gear3d(varargin)

%GEAR3D   GUI example of 3D gear.
%   GEAR3D will pop up a GUI example of 3D gear. The gear rolls on a geared
%   ground based on the mouse location. It uses the x-location of the mouse
%   pointer for the gear location. Use the arrow keys to change the view.
%   Press SPACEBAR to reset the view. This was inspired by Mike Agostini's
%   The gear is made of 2 surface objects, and the ground is a single surface
%   object. Since the moving part (gear) only contains 2 objects, the
%   animation update is quite smooth. It uses OpenGL rendering.
%
%   GEAR3D accepts 3 optional arguments that specify the number of teeth on the
%   gear, number of spokes, and the gear ratio between the ground and the gear.
%
%   Example:
%     GEAR3D('teeth', 30)   - default is 50.
%     GEAR3D('spokes', 4)   - default is 8.
%     GEAR3D('ratio', 2)    - default is 3. This also determines how big
%                             the ground radius is.
%   Only positive integers are allowed.
%
%   This has no practical use. I made it as an exercise for 3d animation.
%   You have been warned. This was created in R13SP1, so nested function is
%   not utilized. Nested function will improve how surface data are passed
%   between functions.
%
%   VERSIONS:
%   v1.0 - first version
%   v1.1 - fixed gear meshing problem. (Feb 2, 2006)
%   v1.2 - changed to pass parameters instead of using handles structure
%          (for speed). also inlined the stripped down version of the ROTATE
%          function to speed up animation (Feb 25, 2006)
%

%   Jiro Doke
%   Feb 3, 2006

%   EngPedia.ir
%   Iranian Engineering Encyclopedia


%--------------------------------------------------------------------------
% Default values
%--------------------------------------------------------------------------

% Number of teeth
numteeth  = 50;
% Number of spokes
numspokes = 8;
% Gear ratio 
rr        = 3;

%--------------------------------------------------------------------------
% Optional arguments
%--------------------------------------------------------------------------

if mod(nargin, 2) == 1
  error('Optional arguments must come in pairs.');
end
if nargin
  opt = varargin(1:2:end);
  val = varargin(2:2:end);
  validOpts = {'teeth', 'spokes', 'ratio'};
  for iArg = 1:length(opt)
    id = strmatch(lower(opt{iArg}), validOpts);
    if isempty(id)
      error('Invalid option. Valid options: ''teeth'', ''spokes'', ''ratio''');
    else
      switch strmatch(lower(opt{iArg}), validOpts)
        
        case 1
          if isnumeric(val{iArg}) & length(val{iArg}) == 1
            numteeth = round(abs(val{iArg}));
          end
          
        case 2
          if isnumeric(val{iArg}) & length(val{iArg}) == 1
            numspokes = round(abs(val{iArg}));
          end
          
        case 3
          if isnumeric(val{iArg}) & length(val{iArg}) == 1
            rr = round(abs(val{iArg}));
          end
          
      end
    end
  end
end

%--------------------------------------------------------------------------
% Construct gear and ground
%--------------------------------------------------------------------------

% Gear part radii
r1 = 1;
r2 = 3;
r3 = 10;
r4 = 11;
r5 = 13;
r6 = 12;

% Radius to the center of gear teeth
r = (r5 + r6) / 2;

% Height of gear teeth
h = r5 - r6;

% Radius to the center of ground teeth
l = r * rr;

% Ground radii
l1 = l  - h/2;
l2 = l  + h/2;
l3 = l2 + 2;

% Gear
[x0,y0,z0]       = cylinder([r6], numteeth*4);  % teeth groove
[x1,y1,z1]       = cylinder([r1, r1, r2, r2, r1], numteeth*4);  % spokes
[x2,y2,z2]       = cylinder([r3, r3, r4, r4, r5, r5, r4, r4, r3], numteeth*4);  % gear teeth
z1([1, 4, 5], :) =  2;
z1(2:3, :)       = -2;
z2([1, 8, 9], :) =  2;
z2(2:3, :)       = -2;
z2(4:5, :)       = -1;
z2(6:7, :)       =  1;
x2(5:6,1:4:end)  = x0(1:2,1:4:end);
x2(5:6,2:4:end)  = x0(1:2,2:4:end);
y2(5:6,1:4:end)  = y0(1:2,1:4:end);
y2(5:6,2:4:end)  = y0(1:2,2:4:end);

% Spoke
interval  = round(length(x1) / numspokes);
for id = 1:4
  x1(3:4, id:interval:end) = x2(1:2, id:interval:end);
  y1(3:4, id:interval:end) = y2(1:2, id:interval:end);
end

% Ground
[x3, y3, z3]         = cylinder([l2, l2, l3, l3, l2], numteeth * rr * 4);
[x4, y4, z4]         = cylinder(l1, numteeth * rr * 4);
z3([1 4 5], :)       =  4;
z3([2 3], :)         = -4;
x3([1 2 5], 1:4:end) = x4([1 1 1], 1:4:end);
x3([1 2 5], 2:4:end) = x4([1 1 1], 2:4:end);
y3([1 2 5], 1:4:end) = y4([1 1 1], 1:4:end);
y3([1 2 5], 2:4:end) = y4([1 1 1], 2:4:end);

% Make ground a half circle
len            = round(length(x3) / 2);
x3(:, len:end) = [];
y3(:, len:end) = [];
z3(:, len:end) = [];

%--------------------------------------------------------------------------
% GUI
%--------------------------------------------------------------------------

% Create figure;
fH = findobj('Type', 'figure', 'Tag', 'solidmodelGUI');
if ishandle(fH)
  close(fH);
end
fH = figure(...
  'Name'       , sprintf('3D Gear: View = [%3.0f, %3.0f]', 0, -50), ...
  'NumberTitle', 'off', ...
  'Units'      , 'normalized', ...
  'Position'   , [.1, .1, .8, .8], ...
  'Visible'    , 'off', ...
  'Tag'        , 'solidmodelGUI');

axes(...
  'Units'   , 'normalized', ...
  'Position', [0, .9, 1, .1], ...
  'XLim'    , [-1, 1], ...
  'YLim'    , [-1, 1], ...
  'Visible' , 'off');
text(0, 0, ...
  {'Move the mouse left and right within the figure window to move the gear.',...
    'Use ARROW keys to change the view. SPACE to reset view.'}, ...
  'HorizontalAlignment' , 'center', ...
  'VerticalAlignment'   , 'middle', ...
  'Color'               , 'red');

axH = axes('Units', 'normalized', ...
  'Position', [0, 0, 1, .9]);

% Gear
%
% Spokes
gearH(1) = surface(x1,y1,z1, ...
  'EdgeColor', [.3, .3, .3], ...
  'EdgeAlpha',  0, ...
  'FaceColor', [.5, .5, 1]);
% Gear Teeth
gearH(2) = surface(x2,y2,z2, ...
  'EdgeColor', [.3, .3, .3], ...
  'EdgeAlpha', .1, ...
  'FaceColor', [.5, .5, 1]);

% Ground
surface(x3,y3,z3, ...
  'EdgeColor', [.3, .3, .3], ...
  'EdgeAlpha', .1, ...
  'FaceColor', [.5, 1, .5], ...
  'FaceAlpha', .5);

set(axH, 'View', [0, -50]);
axis equal manual off;
set(axH, 'CameraViewAngleMode', 'manual');

% Add lighting
light('Position', [50 , 0, -20]);
light('Position', [-50, 0, -20]);

% Calculate size once and pass in as parameter
sz1 = size(x1);
sz2 = size(x2);

set(fH, ...
  'Visible'              , 'on', ...
  'KeyPressFcn'          , {@myKeyPressFcn, axH}, ...
  'WindowButtonMotionFcn', {@myMotionFcn, gearH, x1, x2, y1, y2, r, l, sz1, sz2});

% Set initial position of gear
myMotionFcn(gcf, [], gearH, x1, x2, y1, y2, r, l, sz1, sz2);


%--------------------------------------------------------------------------
% myKeyPressFcn - process key presses to rotate view
%--------------------------------------------------------------------------
function myKeyPressFcn(obj, edata, axH)

k = get(obj, 'CurrentKey');
aZeL = get(axH, 'View');

switch lower(k)
  case 'uparrow'
    aZeL(2) = min([aZeL(2) + 10,  90]);
  case 'downarrow'
    % -90 doesn't work well when rotated left or right
    aZeL(2) = max([aZeL(2) - 10, -89.9999]);
  case 'leftarrow'
    aZeL(1) = max([aZeL(1) - 10, -90]);
  case 'rightarrow'
    aZeL(1) = min([aZeL(1) + 10,  90]);
  case 'space'
    aZeL    = [0, -50];
end

set(axH, 'View', aZeL);
set(obj, 'Name', sprintf('3D Gear: View = [%3.0f, %3.0f]', aZeL));


%--------------------------------------------------------------------------
% myMotionFcn - move mouse to move gear
%--------------------------------------------------------------------------
function myMotionFcn(obj, edata, gearH, x1, x2, y1, y2, r, l, sz1, sz2)

pt = get(obj, 'CurrentPoint');

d = l - r;

% Get center location of gear
x0 = -d + pt(1) * d * 2;
y0 = sqrt(abs(d^2 - x0^2));

% Get amount of gear rotation
th1 = atan2(x0, y0) - pi/2;
th = (th1 - (th1 * (l / r)));

%--------------------------------------------------------------------------
% Rotate gear (from ROTATE)
%--------------------------------------------------------------------------
% Calculate rotation matrix
cosa = cos(-th);
sina = sin(-th);
rot  = [cosa, -sina; sina, cosa]';

newxy1   = [x1(:), y1(:)];
newxy2   = [x2(:), y2(:)];
newxy1   = newxy1 * rot;
newxy2   = newxy2 * rot;
newx1    = x0 + reshape(newxy1(:, 1), sz1);
newy1    = y0 + reshape(newxy1(:, 2), sz1);
newx2    = x0 + reshape(newxy2(:, 1), sz2);
newy2    = y0 + reshape(newxy2(:, 2), sz2);

% Set new position for the gear
set(gearH, {'XData', 'YData'}, {newx1, newy1; newx2, newy2});