KIN_TYP_37 – Delta robot kinematics

The stick kinematics known as delta robot consists of 3 rotary axes arranged at an offset of 120 degrees guiding 2 parallel struts via connecting levers. In turn, these struts guide the tool platform. Tool orientation is constant.

Axis configuration in the NC channel
Axis identifier	X, Y, Z (J1, J2, J3)
Axis index	0, 1, 2
Kinematic structure
	Tool axes	Workpiece axes
NC axes	X, Y, Z	-

Offset dimensions of delta robot kinematics

Offset data of kinematics:

HD offset	param[i]	Description	Unit
HD1	0	Tool offset Z	10 E-4 mm
HD2	1	n.a.	[ - ]
HD3	2	n.a.	[ - ]
HD4	3	Radius of connecting line of bottom joint fixed points	10 E-4 mm
HD5	4	Radius of connecting line of top joint fixed points	10 E-4 mm
HD6	5	Bottom strut/arm length	10 E-4 mm
HD7	6	Top strut/arm length (connecting lever)	10 E-4 mm
HD8	7	Angular offset zero position J1 (ideal zero position of top arm horizontal)	10 E-4°
HD9	8	Angular offset zero position J2 (ideal zero position of top arm horizontal)	10 E-4°
HD10	9	Angular offset zero position J3 (ideal zero position of top arm horizontal)	10 E-4°
HD11	10	Limit of minimum joint angle J1 to J3	10 E-4°
HD12	11	Limit of maximum joint angle J1 to J3	10 E-4°
HD13	12	Z zero offset Cart. workpiece coordinate system	10 E-4 mm

The Cartesian coordinate system lies in the origin of the motor mount. The parameter HD11 can shift the system origin so that it is located below the motor mount and the tool holder platform.

By default, the strut connecting levers must be horizontal in the drive zero position. If this is not the case, the angle zero position can be corrected for the internal kinematic model by the parameters HD8, HD9 and HD10. When all rotary axes move in positive rotation, the TCP moves in negative Z direction.

Example: Connecting lever in horizontal position, drive position: 900000 [ 10 E-4° ]

HD8, HD9, HD10: 900000 [ 10 E-4° ]

Notice

This kinematic transformation was developed in collaboration with Esslingen University (www.hs-esslingen.de).