from
3d Clock with geartrain
by Michael Agostini
A clock built using a general 3d rendering engine which supports shafts, gears, and clock-hands.
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| clockFeatures;
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% ---------------------------------------------------------------------------
% function features = clockFeatures
% ---------------------------------------------------------------------------
% Eventually this data will come from a text file.
% At the moment, the geometry is defined in MATLAB. But with a little
% work it could come out of an xml-style format.
% ---------------------------------------------------------------------------
% Michael Agostini
% Copyright 2005-2009 The MathWorks, Inc.
function feature = clockFeatures;
% Get the current time
current_time = clock ;
second_ratio = round(current_time(6)/60) ;
minute_ratio = current_time(5)/60 ;
second_angle = -second_ratio * 2*pi ;
minute_angle = -(current_time(5)+second_ratio)/60 * 2*pi ;
hour_angle = -(current_time(4)+minute_ratio)/12 * 2*pi ;
% Main rates
second_hand_rate = -1/60 * 2*pi ;
minute_hand_rate = second_hand_rate/60 ;
hour_hand_rate = minute_hand_rate/12 ;
% Coupling rates
sec_to_min_driver1 = -second_hand_rate/2 ;
sec_to_min_driver2 = second_hand_rate/4 ;
sec_to_min_driver3 = -second_hand_rate/12 ;
min_to_hour_driver = -minute_hand_rate/3 ;
% Initialize the part count to zero
n = 0 ;
% Define the shaft objects
% ------------------------
n = n+1 ;
feature(n).type = 'shaft' ;
feature(n).name = 'secondshaft' ;
feature(n).location = [ 0 0 0.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 second_hand_rate] ;
feature(n).facecolor = [ 1 1 0 ] ;
feature(n).innerRad = 0.27 ;
feature(n).outerRad = 0.30 ;
feature(n).length = 10.0 ;
feature(n).numSides = 16 ;
n = n+1 ;
feature(n).type = 'shaft' ;
feature(n).name = 'minuteshaft' ;
feature(n).location = [ 0 0 3.3 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 minute_hand_rate] ;
feature(n).facecolor = [ 1 0 1 ] ;
feature(n).innerRad = 0.32 ;
feature(n).outerRad = 0.35 ;
feature(n).length = 6.3 ;
feature(n).numSides = 16 ;
n = n+1 ;
feature(n).type = 'shaft' ;
feature(n).name = 'hourshaft' ;
feature(n).location = [ 0 0 5.8 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 hour_hand_rate] ;
feature(n).facecolor = [ 0 1 1 ] ;
feature(n).innerRad = 0.37 ;
feature(n).outerRad = 0.40 ;
feature(n).length = 3.2 ;
feature(n).numSides = 16 ;
n = n+1 ;
feature(n).type = 'shaft' ;
feature(n).name = 'secondtominuteshaft1' ;
feature(n).location = [-6.0 0 0.25] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 sec_to_min_driver1] ;
feature(n).facecolor = [ 0 1 1 ] ;
feature(n).innerRad = 0.25 ;
feature(n).outerRad = 0.30 ;
feature(n).length = 7.5 ;
feature(n).numSides = 16 ;
n = n+1 ;
feature(n).type = 'shaft' ;
feature(n).name = 'secondtominuteshaft2' ;
feature(n).location = [-5.0 5 0.25] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 sec_to_min_driver2] ;
feature(n).facecolor = [ 0 1 1 ] ;
feature(n).innerRad = 0.25 ;
feature(n).outerRad = 0.30 ;
feature(n).length = 7.5 ;
feature(n).numSides = 16 ;
n = n+1 ;
feature(n).type = 'shaft' ;
feature(n).name = 'secondtominuteshaft3' ;
feature(n).location = [ 0 6 0.25] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 sec_to_min_driver3] ;
feature(n).facecolor = [ 0 1 1 ] ;
feature(n).innerRad = 0.25 ;
feature(n).outerRad = 0.30 ;
feature(n).length = 7.5 ;
feature(n).numSides = 16 ;
n = n+1 ;
feature(n).type = 'shaft' ;
feature(n).name = 'minutetohourshaft' ;
feature(n).location = [ 6 0 0.25] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 min_to_hour_driver] ;
feature(n).facecolor = [ 0 1 1 ] ;
feature(n).innerRad = 0.25 ;
feature(n).outerRad = 0.30 ;
feature(n).length = 7.5 ;
feature(n).numSides = 16 ;
% Define the fore and back plates objects
% ---------------------------------------
n = n+1 ;
feature(n).type = 'shaft' ;
feature(n).name = 'faceplate' ;
feature(n).location = [ 0 0 7.5 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 0.00] ;
feature(n).facecolor = [ 0 0.5 1 ] ;
feature(n).edgecolor = [ 0 0.7 1 ] ;
feature(n).facealpha = 0.5 ;
feature(n).edgealpha = 0.1 ;
feature(n).innerRad = 0.42 ;
feature(n).outerRad = 12.00 ;
feature(n).length = 0.5 ;
feature(n).numSides = 120 ;
feature(n).static = 1 ;
n = n+1 ;
feature(n).type = 'shaft' ;
feature(n).name = 'backplate' ;
feature(n).location = [ 0 0 0.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 0.00] ;
feature(n).facecolor = [ 0 0.5 1 ] ;
feature(n).edgecolor = [ 0 0.7 1 ] ;
feature(n).edgealpha = 0.5 ;
feature(n).innerRad = 0.32 ;
feature(n).outerRad = 12.00 ;
feature(n).length = 0.5 ;
feature(n).numSides = 120 ;
feature(n).static = 1 ;
% Define the hands of the clock
% -----------------------------
n = n+1 ;
feature(n).type = 'hand' ;
feature(n).name = 'secondhand' ;
feature(n).location = [ 0 0.00 9.7 ] ;
feature(n).orientation = [ 0 0 second_angle ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 second_hand_rate] ;
feature(n).facecolor = [ 1 1 0.1 ] ;
feature(n).innerRad = 0.30 ;
feature(n).outerRad = 0.40 ;
feature(n).thickness = 0.2 ;
feature(n).length = 8.0 ;
feature(n).numSides = 12 ;
n = n+1 ;
feature(n).type = 'hand' ;
feature(n).name = 'minutehand' ;
feature(n).location = [ 0 0.00 9.2 ] ;
feature(n).orientation = [ 0 0 minute_angle ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 minute_hand_rate] ;
feature(n).facecolor = [ 1 0.1 1 ] ;
feature(n).innerRad = 0.35 ;
feature(n).outerRad = 0.45 ;
feature(n).thickness = 0.3 ;
feature(n).length = 7.0 ;
feature(n).numSides = 12 ;
n = n+1 ;
feature(n).type = 'hand' ;
feature(n).name = 'hourhand' ;
feature(n).location = [ 0 0.00 8.5 ] ;
feature(n).orientation = [ 0 0 hour_angle ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 hour_hand_rate] ;
feature(n).facecolor = [ 0.1 1 1 ] ;
feature(n).innerRad = 0.40 ;
feature(n).outerRad = 0.50 ;
feature(n).thickness = 0.4 ;
feature(n).length = 4.0 ;
feature(n).numSides = 12 ;
% Define the gear train
% ---------------------
n = n+1 ;
feature(n).type = 'gear' ;
feature(n).name = 'hourmaingear' ;
feature(n).location = [ 0 0.00 6.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 hour_hand_rate] ;
feature(n).facecolor = [ 0 0.9 0.9 ] ;
feature(n).innerRad = 0.40 ;
feature(n).contactRad = 24/5 ;
feature(n).thickness = 0.5 ;
feature(n).toothheight = 0.2 ;
feature(n).numTeeth = 96 ;
feature(n) = gearTweak(feature(n), 0.75, 3) ;
n = n+1 ;
feature(n).type = 'gear' ;
feature(n).name = 'drivertohourgear' ;
feature(n).location = [ 6 0.00 6.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 min_to_hour_driver] ;
feature(n).facecolor = [ 0 0.5 0.5 ] ;
feature(n).innerRad = 0.30 ;
feature(n).contactRad = 6/5 ;
feature(n).thickness = 0.5 ;
feature(n).toothheight = 0.2 ;
feature(n).numTeeth = 24 ;
n = n+1 ;
feature(n).type = 'gear' ;
feature(n).name = 'driverfromminutegear' ;
feature(n).location = [ 6 0.00 5.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 min_to_hour_driver] ;
feature(n).facecolor = [ 0.0 0.5 0.5 ] ;
feature(n).innerRad = 0.30 ;
feature(n).contactRad = 4.5 ;
feature(n).thickness = 0.5 ;
feature(n).toothheight = 0.2 ;
feature(n).numTeeth = 144 ;
feature(n) = gearTweak(feature(n), 0.75, 3) ;
n = n+1 ;
feature(n).type = 'gear' ;
feature(n).name = 'minutetodrivergear' ;
feature(n).location = [ 0 0.00 5.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 minute_hand_rate] ;
feature(n).facecolor = [ 0.9 0 0.9 ] ;
feature(n).innerRad = 0.35 ;
feature(n).contactRad = 1.5 ;
feature(n).thickness = 0.5 ;
feature(n).toothheight = 0.2 ;
feature(n).numTeeth = 48 ;
n = n+1 ;
feature(n).type = 'gear' ;
feature(n).name = 'minutefromdriver3gear' ;
feature(n).location = [ 0 0.00 4.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 minute_hand_rate] ;
feature(n).facecolor = [ 0.9 0 0.9 ] ;
feature(n).innerRad = 0.35 ;
feature(n).contactRad = 5.0 ;
feature(n).thickness = 0.5 ;
feature(n).toothheight = 0.2 ;
feature(n).numTeeth = 120 ;
feature(n) = gearTweak(feature(n), 0.75, 3) ;
n = n+1 ;
feature(n).type = 'gear' ;
feature(n).name = 'driver3tominutegear' ;
feature(n).location = [ 0 6 4.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 sec_to_min_driver3] ;
feature(n).facecolor = [ 0 0.5 0.5 ] ;
feature(n).innerRad = 0.30 ;
feature(n).contactRad = 1.0 ;
feature(n).thickness = 0.5 ;
feature(n).toothheight = 0.2 ;
feature(n).numTeeth = 24 ;
n = n+1 ;
feature(n).type = 'gear' ;
feature(n).name = 'driver3fromdriver2gear' ;
feature(n).location = [ 0 6 3.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 sec_to_min_driver3] ;
feature(n).facecolor = [ 0 0.5 0.5 ] ;
feature(n).innerRad = 0.30 ;
feature(n).contactRad = sqrt(26)*3/4 ;
feature(n).thickness = 0.5 ;
feature(n).toothheight = 0.2 ;
feature(n).numTeeth = 72 ;
feature(n) = gearTweak(feature(n), 0.75, 3) ;
n = n+1 ;
feature(n).type = 'gear' ;
feature(n).name = 'driver2todriver3gear' ;
feature(n).location = [-5 5 3.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 sec_to_min_driver2] ;
feature(n).facecolor = [ 0 0.5 0.5 ] ;
feature(n).innerRad = 0.30 ;
feature(n).contactRad = sqrt(26)*1/4 ;
feature(n).thickness = 0.5 ;
feature(n).toothheight = 0.2 ;
feature(n).numTeeth = 24 ;
n = n+1 ;
feature(n).type = 'gear' ;
feature(n).name = 'driver2fromdriver1gear' ;
feature(n).location = [-5 5 2.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 sec_to_min_driver2] ;
feature(n).facecolor = [ 0 0.5 0.5 ] ;
feature(n).innerRad = 0.30 ;
feature(n).contactRad = sqrt(26)*2/3 ;
feature(n).thickness = 0.5 ;
feature(n).toothheight = 0.2 ;
feature(n).numTeeth = 120 ;
feature(n) = gearTweak(feature(n), 0.025, 3) ;
n = n+1 ;
feature(n).type = 'gear' ;
feature(n).name = 'driver1todriver2gear' ;
feature(n).location = [-6 0 2.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 sec_to_min_driver1] ;
feature(n).facecolor = [ 0 0.5 0.5 ] ;
feature(n).innerRad = 0.30 ;
feature(n).contactRad = sqrt(26)*1/3 ;
feature(n).thickness = 0.5 ;
feature(n).toothheight = 0.2 ;
feature(n).numTeeth = 60 ;
n = n+1 ;
feature(n).type = 'gear' ;
feature(n).name = 'driver1fromsecondgear' ;
feature(n).location = [-6 0 1.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 sec_to_min_driver1] ;
feature(n).facecolor = [ 0 0.5 0.5 ] ;
feature(n).innerRad = 0.30 ;
feature(n).contactRad = 4.0 ;
feature(n).thickness = 0.5 ;
feature(n).toothheight = 0.2 ;
feature(n).numTeeth = 150 ;
feature(n) = gearTweak(feature(n), 0.25, 3) ;
n = n+1 ;
feature(n).type = 'gear' ;
feature(n).name = 'secondtodriver1gear' ;
feature(n).location = [ 0 0 1.0 ] ;
feature(n).orientation = [ 0 0 0.0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 second_hand_rate] ;
feature(n).facecolor = [ 0.9 0.9 0 ] ;
feature(n).innerRad = 0.30 ;
feature(n).contactRad = 2.0 ;
feature(n).thickness = 0.5 ;
feature(n).toothheight = 0.2 ;
feature(n).numTeeth = 75 ;
% Create the markers for the hours
% --------------------------------
numbers = [1:12] ;
number_radius = 11 ;
numbers_angles = numbers/12*2*pi + pi/2 ;
numbers_xpos = number_radius*cos(numbers_angles) ;
numbers_ypos = number_radius*sin(numbers_angles) ;
numbers_zpos = 7.9*ones(size(numbers)) ;
numbers_location = [ numbers_xpos' numbers_ypos' numbers_zpos'];
numbers_xang = pi/2*ones(size(numbers)) ;
numbers_yang = zeros(size(numbers)) ;
numbers_zang = numbers_angles + 3*pi/2 ;
numbers_orientation = [ numbers_xang' numbers_yang' numbers_zang'];
numbers_length = [ 2.0 2.0 3.5, ...
2.0 2.0 3.5, ...
2.0 2.0 3.5, ...
2.0 2.0 3.1 ];
% Create a template for the numbers
defaultnum = feature(n) ;
defaultnum.type = 'shaft' ;
defaultnum.linearVel = [ 0 0 0 ] ;
defaultnum.angularVel = [ 0.00 0.00 0.00] ;
defaultnum.facecolor = [ 0.2 0.2 0.2 ] ;
defaultnum.innerRad = 0.00 ;
defaultnum.outerRad = 0.20 ;
defaultnum.numSides = 10 ;
defaultnum.static = 1 ;
% Create markers for one through noon
for m = 1:length(numbers)
n = n+1 ;
feature(n) = defaultnum ;
feature(n).name = ['oclock_' num2str(m)] ;
feature(n).location = numbers_location(m,:) ;
feature(n).orientation = numbers_orientation(m,:) ;
feature(n).length = numbers_length(m) ;
end
% Add a custom icon at noon
n = n+1 ;
feature(n).type = 'shaft' ;
feature(n).name = 'noon_oclock' ;
feature(n).location = [ 0 7.7 7.9 ] ;
feature(n).orientation = [ pi/2 pi/4 0 ] ;
feature(n).linearVel = [ 0 0 0 ] ;
feature(n).angularVel = [ 0.00 0.00 0.00] ;
feature(n).facecolor = [ 0.2 0.2 0.2 ] ;
feature(n).innerRad = 0.00 ;
feature(n).outerRad = 0.20 ;
feature(n).length = 0.20 ;
feature(n).numSides = 4 ;
feature(n).static = 1 ;
% ---------------------------------------------------------------------------
% gearTweak()
% ---------------------------------------------------------------------------
% Reorients the gear so that the teeth mesh. Values are tuned by hand
% All this should not be necessary once a proper gear object is defined
% (or implimented).
% ---------------------------------------------------------------------------
function gear = gearTweak(gear, toothAmount, axisNum)
% Compute the radians per tooth
rad_per_tooth = 2*pi / gear.numTeeth ;
% Find the number of radians to tweak the gear
tweak = rad_per_tooth*toothAmount ;
% Tweak the orientation
gear.orientation(axisNum) = gear.orientation(axisNum) + tweak ;
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