LinearDelta3

LinearDelta3_4dof

The "LinearDelta3_4dof" axis group describes a three-dimensional parallel kinematic system with an additional axis of rotation C as shown below:

Axis group LinearDelta3_4dof: 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 the upper spherical joints of the parallelograms with the radius R _BASEat axis position A1 = A2 = A3 = 0 mm.

The xy plane of the MCS is horizontal, i.e. all drive axes are at an identical angle (linear angle a ) to the xy _MCSplane.

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 LinearDelta3_4dof axis group 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 circumcircle formed by the lower spherical joints of the parallelograms with the radius R _{TCP .}

x _TCSand x _MCSare parallel at A4 = 0°.

z _TCSis orientated in the opposite direction to z _MCS.

Zero position of the axes

In the zero position of the drives, the upper ball joints of the parallelogram struts lie in the x-y plane of the MCS.

Axis A1, A2 and A3 must be at the same z-height with the same axis position.

The axis A4 is exactly zero if the axes x _TCSand x _MCSare parallel, i.e. the axis x _TCSpoints in the direction of A1.

The positive direction of movement of the drives is downwards towards the apex of the triangular pyramid.

The positive direction of rotation of A4 corresponds to a mathematical positive rotation around the z _MCSaxis.

Parameters

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

Brief overview of all parameters

Linear angle a (index offset 3, subindex 2)

Angle between base platform and drive axle
Setting range (min. value \| unit \| max. value)			Lenze setting
0	°	90	0 °
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 Limits: > 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 _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) Radius of the circular area formed by the points of application of the three parallelogram struts on the end effector. The centre point within the spherical joints is decisive for the radius. The centre of the circumference corresponds to the zero point of the TCS. Limits: 0 < R _{TCP <}R _BASE
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: > 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