Interpolation Algorithm and Mathematical Model in Automated Welding of Saddle-Shaped Weld

Table 1

The interpolation data.

Interpolation; times	Rotation angle /rad	Coordinate of   /mm	Coordinate of   /mm	Coordinate of   /mm	Pose angle of torch /mm
	0.0000	0.0000	150.0000	600.0000	0.7854
	0.1571	23.4652	148.1533	599.5410	0.7915
	0.3142	46.3525	142.6585	598.2069	0.8093
	0.4712	68.0986	133.6510	596.1230	0.8369
	0.6283	88.1678	121.3525	593.4867	0.8719
	0.7854	106.0660	106.0660	590.5506	0.9107
	0.9425	121.3525	88.1678	587.5998	0.9498
	1.0996	133.6510	68.0986	584.9251	0.9852
	1.2566	142.6585	46.3525	582.7938	1.0135
	1.4137	148.1533	23.4652	581.4212	1.0318
	1.5708	150.0000	0.0000	580.9475	1.0381
	1.7279	148.1533	−23.4652	581.4212	1.0318
	1.8850	142.6585	−46.3525	582.7938	1.0135
	2.0420	133.6510	−68.0986	584.9251	0.9852
	2.1991	121.3525	−88.1678	587.5998	0.9498
	2.3562	106.0660	−106.0660	590.5506	0.9107
	2.5133	88.1678	−121.3525	593.4867	0.8719
	2.6704	68.0986	−133.6510	596.1230	0.8369
	2.8274	46.3525	−142.6585	598.2069	0.8093
	2.9845	23.4652	−148.1533	599.5410	0.7915
	3.1416	0.0000	−150.0000	600.0000	0.7854
	3.2987	−23.4652	−148.1533	599.5410	0.7915
	3.4558	−46.3525	−142.6585	598.2069	0.8093
	3.6128	−68.0986	−133.6510	596.1230	0.8369
	3.7699	−88.1678	−121.3525	593.4867	0.8719
	3.9270	−106.0660	−106.0660	590.5506	0.9107
	4.0841	−121.3525	−88.1678	587.5998	0.9498
	4.2412	−133.6510	−68.0986	584.9251	0.9852
	4.3982	−142.6585	−46.3525	582.7938	1.0135
	4.5553	−148.1533	−23.4652	581.4212	1.0318
	4.7124	−150.0000	0.0000	580.9475	1.0381
	4.8695	−148.1533	23.4652	581.4212	1.0318
	5.0265	−142.6585	46.3525	582.7938	1.0135
	5.1836	−133.6510	68.0986	584.9251	0.9852
	5.3407	−121.3525	88.1678	587.5998	0.9498
	5.4978	−106.0660	106.0660	590.5506	0.9107
	5.6549	−88.1678	121.3525	593.4867	0.8719
	5.8119	−68.0986	133.6510	596.1230	0.8369
	5.9690	−46.3525	142.6585	598.2069	0.8093
	6.1261	−23.4652	148.1533	599.5410	0.7915
	6.2832	0.0000	150.0000	600.0000	0.7854