Delta3_4dof

The axis group "Delta3_4dof" describes three-dimensional parallel kinematics with an additional axis of rotation C as shown below:

Delta3_4dof 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, A4

Tool

x, y, z

C

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.

Degrees of freedom of the MCS, relative to the WCS

The axis group Delta3_4dof can be moved as required and rotated around the z-axis of the WCS.

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 TCS and x MCS are parallel at A4 = 0°.
  • z TCS is orientated in the opposite direction to z MCS .

Zero setting of the drives

  • In the zero position of drives A1, A2 and A3, 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.
  • Axis A4 is in the zero position precisely when the axes x TCS and x MCS are parallel to each other, i.e. the axis x TCS points in the direction of A1.
  • A positive angle for A1 to A3 means that the knee lever moves "upwards".
  • The positive direction of rotation of A4 corresponds to a mathematically positive rotation around the z MCS axis.

 

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 Change only possible 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 Change only possible 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 Change only possible 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 TCP is 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 TCP is 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 Change only possible 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 Change only possible 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 Change only possible 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 Change only possible 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

Coulomb friction A4 (index offset 3, subindex 54)

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

Viscous friction A4 (index offset 3, sub-index 60)

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

Torque pilot control: Minimum parameter5 (index offset 3, subindex 78)

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 parameter6 (index offset 3, subindex 79)

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 parameter7 (index offset 3, subindex 80)

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 +

lrMassLever * (lrCenterOfMassLever - 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

MinimalDynamicParameter 5 : = 1/3 * lrMassCAxis1 * lrLengthCAxis1 2 + 1/12 * lrMassCAxis2 * lrLengthCAxis2 2

MinimalDynamicParameter 6 : =
1/2 * lrMassCAxis1 * lrLengthCAxis1

MinimalDynamicParameter 7 : = lrInertiaCAxis

Related topics

Travel ranges of connected axes

Coordinate systems

Basics of tool management

Consideration of differential gears