stepSize = (pi/180)*(360/3000)

thetaHead = seq(-pi/2,pi/2,stepSize)

thetaTail = -thetaHead

thetaLeg = seq(0,2*pi,stepSize)

# In RPM

MaxSpeed = seq(80,130,.1)

# Max Incline on Y Axis

MaxY = (6.5*pi/180)

# Centripital Acceleration

# http://www.engineeringtoolbox.com/centripetal-acceleration-d_1285.html

A = (2*pi*MaxSpeed/60)^2 * Radius/100

# AA weight is 23g

# AA dimensions are in cm, which is used to determine ABS plastic

# Battery holder mass

# http://data.energizer.com/PDFs/E91.pdf

innerLength = 5.050

innerWidth = 1.450 *2

innerHeight = 1.450

outerLength = innerLength + .5

outerWidth = innerWidth + .5

outerHeight = innerHeight + .5

HolderVolume = (outerLength * outerWidth * outerHeight) – (innerLength * innerWidth * innerHeight)

AA = 23

# ABS plastic weight is .97g/cc

# http://www.stelray.com/reference-tables.html

ABSDensity = .97

# Calulate tail and head weight

# Thickness of 1cm for consistant calculations

tailMass = 2*(AA) + (Radius*(1^2) + (HolderVolume)) *ABSDensity

headMass = tailMass

# Previous Semester’s Robot Mass in grams

# https://www.arxterra.com/spring-2016-velociraptor-project-summary/#Size_Weight

Mass = 657

BodyMass = Mass – tailMass – headMass

HeadPositionX = Radius*cos(thetaHead)

HeadPositionY = Radius*sin(thetaHead)

TailPositionX = -Radius*cos(thetaTail)

TailPositionY = -Radius*sin(thetaTail)

# For moments of mass

TailMassX = TailPositionX * tailMass

TailMassY = TailPositionY * tailMass

HeadMassX = HeadPositionX * headMass

HeadMassY = HeadPositionY * headMass

X_Moment = (TailMassX + HeadMassX) / (tailMass + headMass + BodyMass)

Y_Moment = (TailMassY + HeadMassY) / (tailMass + headMass + BodyMass)

g = 9.8

LeverArm = max(Y_Moment)

# Torque due to gravity (Y Axis)

MaxTorqueHeadY = (headMass/1000) * g * Radius/100

MaxTorqueTailY = (tailMass/1000) * g * Radius/100

# Realistic torque due to gravity

RealisticTorqueHeadY = MaxTorqueHeadY * sin(MaxY)

RealisticTorqueTailY = MaxTorqueTailY * sin(MaxY)

# Torque due to Acceleration (X Axis)

MaxTorqueHeadX = (headMass/1000) * A * Radius/100

MaxTorqueTailX = (tailMass/1000) * A * Radius/100

# Platform Maximum Torque (Y Axis)

MaxTorquePlatform = MaxTorqueHeadY + MaxTorqueTailY + ((headMass/1000) * A * Radius/100) + ((tailMass/1000) * A * Radius/100)

# Frictionless Turning Torque

MaxTurningTorque = ((Mass/1000) * g) * LeverArm/100

# Frictionless Leg Moving Torque

MaxLegTorque = (Mass/2)/1000 * g * LegRadius/100

LegTorque = abs(MaxLegTorque * sin(thetaLeg))

RealMaxLegTorque = abs(MaxLegTorque * sin(60/180 * pi))

Radius2 = 1.5*Radius1

Radius3 = 2.25*Radius1

RPM = 32

w1 = seq(from = 0, to = -2*pi, by = -2*pi/360)

w2 = c(seq(from = 0, to = -(4/3)*pi, by = -(4/3)*pi/(2*length(w1)/3)),seq(from = -(4/3)*pi, to = -2*pi, by = -(2/3)*pi/(1*length(w1)/3)))

w2 = w2[1:length(w1)+1] – 4*pi/3

w3 = c(seq(from = 0, to = -(4/3)*pi, by = -(4/3)*pi/(2*length(w1)/3)),seq(from = (4/3)*pi, to = 0, by = -(2/3)*pi/(1*length(w1)/3)))

w3 = w3[1:length(w1)+1] – 5*pi/6

# ABS plastic weight is .97g/cc

# http://www.stelray.com/reference-tables.html

ABSDensity = .97

# Other side is roughly a quarter of scaling factor in length

massR2 = .5*(Radius2 * .25) * ABSDensity

# Other side is roughly a one and a half quarter of scaling factor in  length

massR3 = .5*(Radius3 * 1.5) * ABSDensity

# Other side is roughly a quarter of lever arm length

mass = 657

bodyMass = mass/2 – 2*(massR2 + massR3)

# Centripital Acceleration

# http://www.engineeringtoolbox.com/centripetal-acceleration-d_1285.html

A2 = (2*pi*RPM/60)^2 * Radius2/100

A3 = (2*pi*RPM/60)^2 * Radius3/100

g = 9.8

LegTorque1 = (bodyMass)/1000 * g * Radius1/100 * sin(w1)

LegTorque2 = ((massR2)/1000 * g * Radius2/100) + ((bodyMass)/1000 * g * Radius2/100 * sin(w2))

LegTorque3 = ((massR3)/1000 * g * Radius3/100) + ((bodyMass)/1000 * g * Radius3/100 * sin(w3))

LegTorque = (LegTorque1 + LegTorque2 + LegTorque3)

plot(w1, LegTorque, col = “black”, type = “o”, pch = NA, lty = 1, lwd = 2, ylab = “Torque (N-m)”, xlab = “Primary Lever Arm Position (Radians)”, main = “Leg Torque Versus Lever Arm Position”)

AverageLT = mean(LegTorque)

TorqueForCurrent = LegTorque

TorqueForCurrent[TorqueForCurrent < 0] = 0

wTip = seq(pi/2, 0,(-pi/2)/360)

TipOverTorque = 6.5/100 * g * (BodyMass/2-2*(massR2 + massR3))/1000

plot(MaxSpeed,2*MaxTorqueHeadX10, cex = .75, ylim = c(0,2*max(MaxTorqueHeadX10)), pch = “.”, col = “green”, xlab = “Servo Speed (RPM)”, ylab = “Servo Torque (N-m)”, main = ” H/T Servo Torque vs RPM at Differing H/T Radii”)

lines(MaxSpeed,2*MaxTorqueHeadX9, pch = “.”, col = “red”)

lines(MaxSpeed,2*MaxTorqueHeadX8, pch = “.”, col = “blue”)

lines(MaxSpeed,2*MaxTorqueHeadX7, pch = “.”, col = “orange”)

lines(MaxSpeed,2*MaxTorqueHeadX6, pch = “.”, col = “brown”)

lines(MaxSpeed,rep(TipOverTorque,length(MaxTorqueHeadX7)),col = “black”)

legend(“topleft”, cex =.75, lty =c(1,1,1,1,1,1), lwd = c(1,1,1,1,1,1), col = c(“green”,”red”,”blue”,”orange”,”brown”,”black”), legend = c(“R = 10cm”,”R = 9cm”,”R = 8cm”,”R = 7cm”,”R = 6cm”, “Tip Over Torque”))

thetaPlatform = seq(-6.5*pi/180, 6.5*pi/180, 1/360)

HeadPlatformPositionZ7 = 7*sin(thetaPlatform)

TailPlatformPositionZ7 = -7*sin(thetaPlatform)

HeadPlatformPositionZ6 = 6*sin(thetaPlatform)

TailPlatformPositionZ6 = -6*sin(thetaPlatform)

HeadPlatformPositionZ8 = 8*sin(thetaPlatform)

TailPlatformPositionZ8 = -8*sin(thetaPlatform)

HeadPlatformPositionZ9 = 9*sin(thetaPlatform)

TailPlatformPositionZ9 = -9*sin(thetaPlatform)

HeadPlatformPositionZ10 = 10*sin(thetaPlatform)

TailPlatformPositionZ10 = -10*sin(thetaPlatform)

plot(HeadPlatformPositionZ10, thetaPlatform*180/pi, cex = .75, xlim = c(min(TailPlatformPositionZ10),max(HeadPlatformPositionZ10)), type = “o”, pch = NA, col = “green”, xlab = “Head and Tail Position Z Axis (cm)”, ylab = “Platform Inclination (degrees)”, main = “H/T Position vs Inclination Angle”)

lines(HeadPlatformPositionZ9, thetaPlatform*180/pi, pch = “.”, col = “red”)

lines(HeadPlatformPositionZ8, thetaPlatform*180/pi, pch = “.”, col = “blue”)

lines(HeadPlatformPositionZ7, thetaPlatform*180/pi, pch = “.”, col = “orange”)

lines(HeadPlatformPositionZ6, thetaPlatform*180/pi, pch = “.”, col = “brown”)

lines(TailPlatformPositionZ10, thetaPlatform*180/pi, pch = “.”, col = “green”)

lines(TailPlatformPositionZ9, thetaPlatform*180/pi, pch = “.”, col = “red”)

lines(TailPlatformPositionZ8, thetaPlatform*180/pi, pch = “.”, col = “blue”)

lines(TailPlatformPositionZ7, thetaPlatform*180/pi, pch = “.”, col = “orange”)

lines(TailPlatformPositionZ6, thetaPlatform*180/pi, pch = “.”, col = “brown”)

legend(“topleft”, cex =.75, lty =c(1,1,1,1,1,1), lwd = c(1,1,1,1,1,1), col = c(“green”,”red”,”blue”,”orange”,”brown”), legend = c(“R = 10cm”,”R = 9cm”,”R = 8cm”,”R = 7cm”,”R = 6cm”))

ADC = seq(0,3.3,.00080)

ADC = c(ADC, rep(3.3, length(ADC)*(1/12)))

ADCRad = seq(0,2*pi, 2*pi/length(ADC))

ADCRad = ADCRad[1:length(ADCRad)-1]

plot(ADCRad, ADC, col = “black”, type = “l”, pch = NA, lty = 1, lwd = 2,  ylab = “ADC Voltage (V)”, xlab = “Primary Lever Arm Position (Radians)”, main = “A/D Voltage Versus Shaft Position”)