Difference between revisions of "Tutorials/Arduino Projects/Additional Info/Turning Calculations"

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(Differential Steering)
 
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== Differential Steering ==
 
== Differential Steering ==
  
For a differential drive system, the "center point" where all the turning calculations are based from is based on the location of all the various driving wheels. To keep the process simple, we recommend that you try to keep the wheels evenly spaced so the center is just half way between all the wheels. If the system has a caster, then you can just ignore it for simplicity. <strike>So say you had 6 drive wheels equally spaced, then the "center" would be half way between the two center wheels. However if the wheels are not evenly spaced then you need to do some math. Say the 6 wheels were placed so that the front wheels are 7 in from the center wheels and the back wheels are only 4 in from the center. In this instance you would find the average. you could say that the front wheels are +7, the center are 0, and the back wheels are -4. If you take the average you find that the "center" is at +1 from the center wheels.</strike>
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For a differential drive system, the "center point" where all the turning calculations are based from is based on the location of all the various driving wheels. To keep the process simple, we recommend that you try to keep the wheels evenly spaced so the center is just half way between all the wheels. If the system has a caster, then you can just ignore it for simplicity.  
 
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For the calculations we will say that the distance between the wheels from one side to the other is W. We will also say that the desired swing radius from the center is R, and the desired speed is V. The speed of the left side will be defined as V<sub>L</sub> and the speed of the right side as V<sub>R</sub>.
 
For the calculations we will say that the distance between the wheels from one side to the other is W. We will also say that the desired swing radius from the center is R, and the desired speed is V. The speed of the left side will be defined as V<sub>L</sub> and the speed of the right side as V<sub>R</sub>.
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[[image:Differential_Steering_Graphic_4_wheels.png|thumb|c|center|400px|]]
 
[[image:Differential_Steering_Graphic_4_wheels.png|thumb|c|center|400px|]]
 
[[image:Differential_Steering_Graphic_2_wheels.png|thumb|c|center|400px|]]
 
[[image:Differential_Steering_Graphic_2_wheels.png|thumb|c|center|400px|]]
[[image:Differental_Steering_R_Equation.png|center|]]
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[[image:Differential_Steering_R_Equation.png|center|]]
[[image:Differental_Steering_V_Equation.png|center|]]
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[[image:Differential_Steering_V_Equation.png|center|]]
[[image:Differental_Steering_VL_Equation.png|center|]]
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[[image:Differential_Steering_VL_Equation.png|center|]]
[[image:Differental_Steering_VR_Equation.png|center|]]
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[[image:Differential_Steering_VR_Equation.png|center|]]
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{{Todo|Could add Kinematic equations for (X,Y) and robot orientation angle.}}
  
== Akerman Steering ==
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== Ackermann Steering ==
Akerman steering is the steering system used in just about every automobile. Normally the center point is located between a pair of fixed wheels. However this system can have the "center point" located anywhere you want. We will define the distance from the center point to the wheel length-wise as H. We will also define the turning radius as R. We will define the angle of the left and right wheels as Θ<sub>L</sub> and Θ<sub>R</sub> respectively. We will also define W as the distance between the wheels on each side.
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Ackermann steering is the steering system used in just about every automobile. Normally the center point is located between a pair of fixed wheels. However this system can have the "center point" located anywhere you want. We will define the distance from the center point to the wheel length-wise as H. We will also define the turning radius as R. We will define the angle of the left and right wheels as Θ<sub>L</sub> and Θ<sub>R</sub> respectively. We will also define W as the distance between the wheels on each side.
  
[[image:Akerman_Steering_Graphic.png|thumb|c|center|400px|]]
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[[image:Ackermann_Steering_Graphic.png|thumb|c|center|400px|]]
[[image:Akerman_Steering_Left_angle.png|center|]]
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[[image:Ackermann_Steering_Left_angle.png|center|]]
[[image:Akerman_Steering_Right_angle.png|center|]]
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[[image:Ackermann_Steering_Right_angle.png|center|]]
  
 
{{Note|you can add additional pivoting wheels. Just change the value of H to the distance for those wheels.}}
 
{{Note|you can add additional pivoting wheels. Just change the value of H to the distance for those wheels.}}
  
[[Category:need to be finished]]
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{{Todo|Could add Kinematic equations for (X,Y) and robot orientation angle.}}

Latest revision as of 18:51, 8 August 2012

Turning calculations
Turning calculations
ArduinoArduino Tutorials and Guided Projects → Turning calculations

Differential Steering

For a differential drive system, the "center point" where all the turning calculations are based from is based on the location of all the various driving wheels. To keep the process simple, we recommend that you try to keep the wheels evenly spaced so the center is just half way between all the wheels. If the system has a caster, then you can just ignore it for simplicity.

For the calculations we will say that the distance between the wheels from one side to the other is W. We will also say that the desired swing radius from the center is R, and the desired speed is V. The speed of the left side will be defined as VL and the speed of the right side as VR.

Differential Steering Graphic 4 wheels.png
Differential Steering Graphic 2 wheels.png
Differential Steering R Equation.png
Differential Steering V Equation.png
Differential Steering VL Equation.png
Differential Steering VR Equation.png

Notepad.gif TODO: Could add Kinematic equations for (X,Y) and robot orientation angle.

Ackermann Steering

Ackermann steering is the steering system used in just about every automobile. Normally the center point is located between a pair of fixed wheels. However this system can have the "center point" located anywhere you want. We will define the distance from the center point to the wheel length-wise as H. We will also define the turning radius as R. We will define the angle of the left and right wheels as ΘL and ΘR respectively. We will also define W as the distance between the wheels on each side.

Ackermann Steering Graphic.png
Ackermann Steering Left angle.png
Ackermann Steering Right angle.png

Notepad.gif NOTE: you can add additional pivoting wheels. Just change the value of H to the distance for those wheels.

Notepad.gif TODO: Could add Kinematic equations for (X,Y) and robot orientation angle.