Positioning Accuracy and Numerical Analysis of the Main Casting Mechanism of the Hybrid Casting Robot

Table 1

Chain 1 coordinate transformation parameters and physical significance.

Branched chain	Coordinate transformation	(Δ) aei,(j−1)j	(Δ) αei,(j−1)j	(Δ) dei,j	(Δ) θei,j	“Δ” physical meaning
Branched chain 1	e1O ⟶ e10	(Δ) ae1,O0	(Δ) αe1,O0	(Δ) de1,0	(Δ) θe1,0	Installation error of upper (fixed) platform
	e10 ⟶ e11	(Δ) ae1, 01	(Δ) αe1, 01	(Δ) de1,1	(Δ) θe1,1	Error of universal joint 1
	e11 ⟶ e12	(Δ) ae1,12	(Δ) αe1,12	(Δ) de1,2	(Δ) θe1,2	Error of universal joint 1
	e12 ⟶ e13	(Δ) ae1,23	(Δ) αe1,23	(Δ) de1,3	(Δ) θe1,3	The error of length rod
	e13 ⟶ e14	(Δ) ae1,34	(Δ) αe1,34	(Δ) de1,4	(Δ) θe1,4	The error of moving long rod
	e14 ⟶ e15	(Δ) ae1,45	(Δ) αe1,45	(Δ) de1,5	(Δ) θe1,5	Error of universal joint 2
	e15 ⟶ e16	(Δ) ae1,56	(Δ) αe1,56	(Δ) de1,6	(Δ) θe1,6	Error of universal joint 2
	e16 ⟶ e1o	(Δ) ae1,6o	(Δ) αe1,6o	(Δ) de1,o	(Δ) θe1,o	Installation error of lower (moving) platform