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.
• Torque (Force) is always expressed in [Nm] ([N])
  

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	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}	Total moment of inertia around the rotation axis of the moved part
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 L^2}	Square of length of crank arm (axis to payload)

Model equation

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 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	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}	Total moment of inertia around the rotation axis of the moved part
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 L^2}	Square of length of crank arm (axis to payload)
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 \cdot g \cdot A}	Mass (without payload) * Gravity * Distance to center of mass
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 g \cdot L}	Gravity * Distance to Payload

Model equation

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 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	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}	Total mass of the moved part.

Model equation

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

Dynamic Model 2 - vertical or tilted axis

Vertical linear axis

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 M}	Total mass of the moved part.
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 M \cdot g \cdot \cos(\alpha)}	Constant force due to gravity.
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 g \cdot \cos(\alpha)}	Gravity coefficient used to consider payload mass. (g = 9.80665)

Model equation

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 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	$J_{2}$
4	$L_{1}\cdot A_{2}\cdot M_{2}$
5	$M_{3}$
6	$g\cdot M_{3}$
7	$I_{4}$
8	$J_{4}$

Delta Robots

Dynamic Model 1

Delta robot

Number	Parameter	Comments
1	$\Theta _{AB}$	kg*m2
2	$g\cdot L_{AB}\cdot M_{AB}$	kg*m2/sec2
3	$M_{BC}$	kg
4	$\Theta _{BC}$	kg*m2
5	$M_{P}$	kg
6	$M_{T}$	kg
7	$\Theta _{T}$	kg*m2
8	$\Theta _{T\phi }$	kg*m2
9	$L_{TO}$	m
10	$L_{TP}$	m
11	$D$
12	$C_{r}$
13	$Fr_{max}$
14	$R_{ext}$

Galileo Spherical Robots (GSR) =

Dynamic Model 1

Galileo robot

Number	Parameter	Comments
1	mP	Payload mass [kg]
2	mB	Balance mass [kg]
3	TP	Payload mass center distance from the flange [mm]
4	TB	Balance mass center distance from the (0,0) [mm]
5	IR	Inertia of the payload around roll [kg*m2