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Time Domain Spirograph
Since Motors will be relatively close (<5cm), propogation time can be neglected
In[7002]:=
In[7003]:=
In[7004]:= Φstep = 2 Π � 100;
ratios = Table@1 � If@j ¹ 0, j, 1D, 8j, -5, 5, .1<D;
ratios
motor1RPM = 1800;
motor2RPM = -1500;
motor3RPM = 1800;
Θ1deg = 2;
Θ2deg = 2;
Θ3deg = 2;
maxTime = 1;
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In[7014]:= Length@ratiosDOut[7014]= 101
In[7015]:= Length@ratiosDOut[7015]= 101
Printed by Wolfram Mathematica Student Edition
In[7016]:=
Θ1 = Θ1deg * Π � 180;
Θ2 = Θ2deg * Π � 180;
Θ3 = Θ3deg * Π � 180;
Γdeg = 180;
Γ = Γdeg * Π � 180;
xHat = 81, 0, 0<;
origin = 80, 0, 0<;
normalM1@Θ_, Φ_D := 8Cos@ΘD, Sin@ΦD Sin@ΘD, Cos@ΦD Sin@ΘD<;
normalM2@Θ_, Φ_D := 8-Cos@ΘD, Sin@ΦD Sin@ΘD, Cos@ΦD Sin@ΘD<;
normalM3@Θ_, Φ_D := 8Cos@ΘD, Sin@ΦD Sin@ΘD, Cos@ΦD Sin@ΘD<;
CrossMatM1@Θ_, Φ_D := 880, -normalM1@Θ, ΦD@@3DD, normalM1@Θ, ΦD@@2DD<,
8normalM1@Θ, ΦD@@3DD, 0, -normalM1@Θ, ΦD@@1DD<,
8-normalM1@Θ, ΦD@@2DD, normalM1@Θ, ΦD@@1DD, 0<<;
CrossMatM2@Θ_, Φ_D := 880, -normalM2@Θ, ΦD@@3DD, normalM2@Θ, ΦD@@2DD<,
8normalM2@Θ, ΦD@@3DD, 0, -normalM2@Θ, ΦD@@1DD<,
8-normalM2@Θ, ΦD@@2DD, normalM2@Θ, ΦD@@1DD, 0<<;
CrossMatM3@Θ_, Φ_D := 880, -normalM3@Θ, ΦD@@3DD, normalM3@Θ, ΦD@@2DD<,
8normalM3@Θ, ΦD@@3DD, 0, -normalM3@Θ, ΦD@@1DD<,
8-normalM3@Θ, ΦD@@2DD, normalM3@Θ, ΦD@@1DD, 0<<;
RotM1@Θ_, Φ_, Γ_D := IdentityMatrix@3D * Cos@ΓD + Sin@ΓD CrossMatM1@Θ, ΦD +
H1 - Cos@ΓDL TensorProduct@normalM1@Θ, ΦD, normalM1@Θ, ΦDD;
RotM2@Θ_, Φ_, Γ_D := IdentityMatrix@3D * Cos@ΓD + Sin@ΓD CrossMatM2@Θ, ΦD +
H1 - Cos@ΓDL TensorProduct@normalM2@Θ, ΦD, normalM2@Θ, ΦDD;
RotM3@Θ_, Φ_, Γ_D := IdentityMatrix@3D * Cos@ΓD + Sin@ΓD CrossMatM3@Θ, ΦD +
H1 - Cos@ΓDL TensorProduct@normalM3@Θ, ΦD, normalM3@Θ, ΦDD;
incident = :- 3 � 2, 1 � 2, 0>;
motor1Rads = 2 Π motor1RPM � 60;
motor2Rads = 2 Π motor2RPM � 60;
motor3Rads = 2 Π motor3RPM � 60;
Φ2@Φ_D := motor2RadsΦ
motor1Rads
;
Φ3@Φ_D := motor3RadsΦ
motor1Rads
;
mirrorXSep = 0.025;
mirrorYSep = 0.025;
mirrorRadius = .012;
projectionDist = 1;
ΦProg = Table@j, 8j, 0, maxTime + Φstep � motor1Rads, Φstep � motor1Rads<D;
m2Plot = Table@j, 8j, 0, maxTime + Φstep � motor1Rads, Φstep � motor1Rads<D;
m3Plot = Table@j, 8j, 0, maxTime + Φstep � motor1Rads, Φstep � motor1Rads<D;
projectionPlot = Table@j, 8j, 0, maxTime + Φstep � motor1Rads, Φstep � motor1Rads<D;
m2IncidentPlot = Table@j, 8j, 0, maxTime + Φstep � motor1Rads, Φstep � motor1Rads<D;
m3IncidentPlot = Table@j, 8j, 0, maxTime + Φstep � motor1Rads, Φstep � motor1Rads<D;
projectionIncidentPlot =
Table@j, 8j, 0, maxTime + Φstep � motor1Rads, Φstep � motor1Rads<D;
2 Untitled-3
Printed by Wolfram Mathematica Student Edition
In[7049]:= DoB:
Φ2@Φ_D := motor1Rads * ratios@@kDDΦ
motor1Rads
,
t = 0;
Φ1 = 0;
runs = 0;
WhileBt £ maxTime,
:reflectionM1 = -RotM1@Θ1, Φ1, ΓD.incident,
m2IncidentPos = reflectionM1 * mirrorXSep � Abs@reflectionM1@@1DDD,
reflectionM2 = -RotM2@Θ2, Φ2@Φ1D, ΓD.reflectionM1,
m3IncidentPos = m2IncidentPos +
mirrorXSep
Abs@reflectionM2@@1DDD* reflectionM2,
m3IncidentPlot@@Φ1 � Φstep + 1DD = 8m3IncidentPos@@2DD, m3IncidentPos@@3DD<,
H*reflectionM3=-RotM3@Θ3,Φ3@Φ1D,ΓD.reflectionM2,
projectedPos=m3IncidentPos+projectionDist
Abs@reflectionM3@@1DDD *reflectionM3,
m2Plot@@Φ1�Φstep+1DD=m2IncidentPos,
m3Plot@@Φ1�Φstep+1DD=m3IncidentPos,
projectionPlot@@Φ1�Φstep+1DD=projectedPos,
m2IncidentPlot@@Φ1�Φstep+1DD=8m2IncidentPos@@2DD,m2IncidentPos@@3DD<,
projectionIncidentPlot@@Φ1�Φstep+1DD=
8projectedPos@@2DD,projectedPos@@3DD<,*L
t =
Φ1
motor1Rads
,
runs += 1;
Φ1 += Φstep>
F,
ListLinePlot@m3IncidentPlot, PlotLabel ® ratios@@kDDD �� Print>,
8k, 1, Length@ratiosD<F
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