Dynamic Models

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	$I$	Total moment of inertia around the rotation axis of the moved part

Model equation

$T=(I+I_{payload})\cdot acc$

Dynamic Model 2 - horizontal crank-arm axis

Horizontal crank-arm axis

Number	Parameter	Comments
1	$I$	Total moment of inertia around the rotation axis of the moved part
2	$L^{2}$	Square of length of crank arm (axis to payload)

Model equation

$T=(I+I_{payload}+L^{2}\cdot M_{payload})\cdot acc$

Dynamic Model 3 - vertical crank-arm axis

Vertical crank-arm axis

Number	Parameter	Comments
1	$I$	Total moment of inertia around the rotation axis of the moved part
2	$L^{2}$	Square of length of crank arm (axis to payload)
3	$M\cdot g\cdot A$	Mass (without payload) * Gravity * Distance to center of mass
4	$g\cdot L$	Gravity * Distance to Payload

Model equation

$T=(I+I_{payload}+L^{2}\cdot M_{payload})\cdot acc-(M\cdot g\cdot A+M_{payload}\cdot g\cdot L)\cdot \sin(pos)$

Linear Axes

Dynamic Model 1 - horizontal axis

Horizontal linear axis

Number	Parameter	Comments
1	$M$	Total mass of the moved part.

Model equation

$T=(M+M_{payload})\cdot acc$

Dynamic Model 2 - vertical or tilted axis

Vertical linear axis

Number	Parameter	Comments
1	$M$	Total mass of the moved part.
2	$M\cdot g\cdot \cos(\alpha )$	Constant force due to gravity.
3	$g\cdot \cos(\alpha )$	Gravity coefficient used to consider payload mass. (g = 9.80665)

Model equation

$T=(M+M_{payload})\cdot acc+M\cdot g\cdot \cos(\alpha )+M_{payload}\cdot g\cdot \cos(\alpha )$

Traverse Arm Robots

Dynamic Model 1

Traverse Arm robot

Number	Parameter	Comments
1	$M_{1}+M_{2}$
2	$A_{2}\cdot M_{2}$
3	$A_{2}^{2}\cdot M_{2}+I_{2}$
4	$M_{3}$
5	$g\cdot M_{3}$
6	$I_{4}$
7	$J_{4}$

Scara Robots

Dynamic Model 1

Number	Parameter	Comments
1	$L_{1}^{2}\cdot M_{2}+I_{1}$
2	$A_{2}^{2}\cdot M_{2}+I_{2}$
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	$L_{TP}$
11	$D$
12	$C_{r}$
13	$Fr_{max}$
14	$R_{ext}$