Difference between revisions of "Dynamic Models"

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|Total moment of inertia around the rotation axis of the moved part
 
|Total moment of inertia around the rotation axis of the moved part
 
|}
 
|}
 +
;Model equation
 +
: <math>T = (I + I_{payload}) \cdot acc</math>
  
 
<br style="clear: both" />
 
<br style="clear: both" />
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|Square of length of crank arm (axis to payload)
 
|Square of length of crank arm (axis to payload)
 
|}
 
|}
 +
;Model equation
 +
: <math>T = (I + I_{payload} + L^2 \cdot M_{payload}) \cdot acc</math>
  
 
<br style="clear: both" />
 
<br style="clear: both" />
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|Gravity * Distance to Payload
 
|Gravity * Distance to Payload
 
|}
 
|}
 +
;Model equation
 +
: <math>T = (I + I_{payload} + L^2 \cdot M_{payload}) \cdot acc - (M \cdot g \cdot A + M_{payload} \cdot g \cdot L) \cdot \sin(pos)</math>
  
 
== Linear Axes ==
 
== Linear Axes ==
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|Total mass of the moved part.
 
|Total mass of the moved part.
 
|}
 
|}
 +
;Model equation
 +
: <math>T = (M + M_{payload}) \cdot acc</math>
  
 
<br style="clear: both" />
 
<br style="clear: both" />
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|Gravity coefficient used to consider payload mass. ('''g = 9.80665''')
 
|Gravity coefficient used to consider payload mass. ('''g = 9.80665''')
 
|}
 
|}
 +
;Model equation
 +
: <math>T = (M + M_{payload}) \cdot acc + M \cdot g \cdot \cos(\alpha) + M_{payload} \cdot g \cdot \cos(\alpha)</math>
  
  

Revision as of 13:33, 31 October 2012

This page gives an overview over all implemented dynamic models.

General considerations

  • Friction is handled on axis basis. The parameters for friction are set for each axis separately.

Rotational Axes

Dynamic Model 1 - simple rotary axis

Number Parameter Comments
1 Total moment of inertia around the rotation axis of the moved part
Model equation


Dynamic Model 2 - horizontal crank-arm axis

Horizontal crank-arm axis
Number Parameter Comments
1 Total moment of inertia around the rotation axis of the moved part
2 Square of length of crank arm (axis to payload)
Model equation


Dynamic Model 3 - vertical crank-arm axis

Vertical crank-arm axis
Number Parameter Comments
1 Total moment of inertia around the rotation axis of the moved part
2 Square of length of crank arm (axis to payload)
3 Mass (without payload) * Gravity * Distance to center of mass
4 Gravity * Distance to Payload
Model equation

Linear Axes

Dynamic Model 1 - horizontal axis

Horizontal linear axis
Number Parameter Comments
1 Total mass of the moved part.
Model equation


Dynamic Model 2 - vertical or tilted axis

Vertical linear axis
Number Parameter Comments
1 Total mass of the moved part.
2 Constant force due to gravity.
3 Gravity coefficient used to consider payload mass. (g = 9.80665)
Model equation


Traverse Arm Robots

Dynamic Model 1

Traverse Arm robot
Number Parameter Comments
1
2
3
4
5
6 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle I_4}
7 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle J_4}


Scara Robots

Dynamic Model 1

Number Parameter Comments
1 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle L_1^2 \cdot M_2 + I_1}
2 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle A_2^2 \cdot M_2 + I_2}
3 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle J_2}
4 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle L_1 \cdot A_2 \cdot M_2}
5 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle M_3}
6 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle g \cdot M_3}
7 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle I_4}
8 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle J_4}


Delta Robots

Dynamic Model 1

Delta robot
Number Parameter Comments
1 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \Theta_{AB}}
2 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle g \cdot L_{AB} \cdot M_{AB}}
3 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle M_{BC}}
4 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \Theta_{BC}}
5 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle M_P}
6 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle M_T}
7 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \Theta_T}
8 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \Theta_{T\phi}}
9 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle L_{TO}}
10 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle L_{TP}}
11 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle D}
12 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle C_r}
13 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Fr_{max}}
14 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle R_{ext}}
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