Delta3_3dof

The axis group "Delta3_3dof" describes three-dimensional parallel kinematics as shown below:

Delta3_3dof axle group: Overview / Mechanic data

Axis legend: x - red y - green z - blue

Degrees of freedom (dof)

Degrees of freedom (dof)	Translation	Rotation
Drives	-	A1, A2, A3
Tool	x, y, z	-

Location of the MCS

The origin lies in the centre of the circumcircle formed by A1, A2 and A3 with the radius R _{BASE .}

The drives are located in the x-y plane.

x-axis points in the direction of A1.

z-axis points "upwards" away from the end effector.

Location of the TCS

The origin lies in the centre of the circumference formed by the passive ball joints with the radius R _{TCP .}

x _TCSand x _MCSare parallel.

z _TCSis orientated in the opposite direction to z _MCS.

Zero setting of the drives

In the zero position of the drives, the toggle levers are "horizontal", i.e. the passive ball joints between the toggle lever and parallelograms are in the x-y plane of the MCS.

A positive angle for A1 to A3 means that the knee lever moves "upwards".

Parameters

A complete list of all kinematics-independent parameters can be found in the section

Brief overview of all parameters

Arm length L1 (index offset 3, subindex 2)

Length of the knee lever (L1) Limits: L1 > 0
Setting range (min. value \| unit \| max. value)			Lenze setting
0	mm	2147483647	0 mm
Read access Write access Can only be changed in "GroupDisabled" state No download				FLOAT_64

Arm length L2 (index offset 3, subindex 3)

Length of the parallelogram (L2) Limits: L2 > 0
Setting range (min. value \| unit \| max. value)			Lenze setting
0	mm	2147483647	0 mm
Read access Write access Can only be changed in "GroupDisabled" state No download				FLOAT_64

Base radius Rbase (index offset 3, subindex 4)

Radius of the base platform (R _BASE) Limits: R _{Base >}R _TCP
Setting range (min. value \| unit \| max. value)			Lenze setting
0	mm	2147483647	0 mm
Read access Write access Can only be changed in "GroupDisabled" state No download				FLOAT_64

End effector radius Rtcp (index offset 3, subindex 5)

Radius of the end effector (R _TCP) Parameterisation option 1: R _TCPis set to the horizontal distance of the TCS to the centre of the ball joints on the parallelogram (radius of the circumference through the ball joints). In this case, the parallelogram width D must be set to the distance between the parallelogram struts. Parameterisation option 2: R _TCPis set to the horizontal distance of the TCS to the centre of the parallelograms (radius of the circumcircle of the parallelogram centres). In this case, the parallelogram width D must be set to zero. Limits: R _{Base >}R _{TCP >}0
Setting range (min. value \| unit \| max. value)			Lenze setting
0	mm	2147483647	0 mm
Read access Write access Can only be changed in "GroupDisabled" state No download				FLOAT_64

Parallelogram width D (index offset 3, subindex 6)

Distance between the parallelogram struts (D) Limits: D >= 0
Setting range (min. value \| unit \| max. value)			Lenze setting
0	mm	2147483647	0 mm
Read access Write access Can only be changed in "GroupDisabled" state No download				FLOAT_64

Coulomb friction A1 (index offset 3, sub-index 51)

Setting range (min. value \| unit \| max. value)			Lenze setting
0	Nm	2147483647	0 Nm
Read access Write access Can only be changed in "GroupDisabled" state No download				FLOAT_64

Coulomb friction A2 (index offset 3, sub-index 52)

Setting range (min. value \| unit \| max. value)			Lenze setting
0	Nm	2147483647	0 Nm
Read access Write access Can only be changed in "GroupDisabled" state No download				FLOAT_64

Coulomb friction A3 (index offset 3, sub-index 53)

Setting range (min. value \| unit \| max. value)			Lenze setting
0	Nm	2147483647	0 Nm
Read access Write access Change only possible in "GroupDisabled" state No download				FLOAT_64

Viscous friction A1 (index offset 3, sub-index 57)

Setting range (min. value \| unit \| max. value)			Lenze setting
0	Nm/(wheel/s)	2147483647	0 Nm/(wheel/s)
Read access Write access Change only possible in "GroupDisabled" state No download				FLOAT_64

Viscous friction A2 (index offset 3, sub-index 58)

Setting range (min. value \| unit \| max. value)			Lenze setting
0	Nm/(wheel/s)	2147483647	0 Nm/(wheel/s)
Read access Write access Change only possible in "GroupDisabled" state No download				FLOAT_64

Viscous friction A3 (index offset 3, sub-index 59)

Setting range (min. value \| unit \| max. value)			Lenze setting
0	Nm/(wheel/s)	2147483647	0 Nm/(wheel/s)
Read access Write access Change only possible in "GroupDisabled" state No download				FLOAT_64

Gravity x (index offset 3, subindex 71)

Setting range (min. value \| unit \| max. value)			Lenze setting
-10	m/s²	10	0 m/s²
Read access Write access Change only possible in "GroupDisabled" state No download				FLOAT_64

Gravity y (index offset 3, subindex 72)

Setting range (min. value \| unit \| max. value)			Lenze setting
-10	m/s²	10	0 m/s²
Read access Write access Change only possible in "GroupDisabled" state No download				FLOAT_64

Gravity z (index offset 3, subindex 73)

Setting range (min. value \| unit \| max. value)			Lenze setting
-10	m/s²	10	-9.81 m/s²
Read access Write access Change only possible in "GroupDisabled" state No download				FLOAT_64

Torque pilot control: Minimum parameter1 (index offset 3, subindex 74)

Setting range (min. value \| unit \| max. value)		Lenze setting
0	2147483647	0
Read access Write access Change only possible in "GroupDisabled" state No download			FLOAT_64

Torque pilot control: Minimum parameter2 (index offset 3, subindex 75)

Setting range (min. value \| unit \| max. value)		Lenze setting
0	2147483647	0
Read access Write access Change only possible in "GroupDisabled" state No download			FLOAT_64

Torque pilot control: Minimum parameter3 (index offset 3, subindex 76)

Setting range (min. value \| unit \| max. value)		Lenze setting
0	2147483647	0
Read access Write access Change only possible in "GroupDisabled" state No download			FLOAT_64

Torque pilot control: Minimum parameter4 (index offset 3, subindex 77)

Setting range (min. value \| unit \| max. value)		Lenze setting
0	2147483647	0
Read access Write access Change only possible in "GroupDisabled" state No download			FLOAT_64

A minimum parameter of the dynamics describes a mathematical summary of several physical masses, mass inertias and geometric lengths that lead to a robustly identifiable parameter set and a computationally efficient calculation rule for feedforward control.

MinimalDynamicParameter 2 : = (lrMassLever + lrMassRhomboid) * lrL1 +
MinimalDynamicParameter 3 : = lrMassRhomboid	The minimum parameter 3 is identical to the mass of the parallelogram
MinimalDynamicParameter 4 : = lrMassTCP	The minimum parameter 4 is identical to the end effector mass