TABLE 1.

Forces (F, in cN) and moments (M, in cNmm) at the final positions of 4.5 mesial and 4.5 distal rotations. When the test tooth is 4.5 mesial rotated, forces and moments are created to disto-rotate the tooth (Mx positive).

	Attachment	x-Axis				y-Axis				z-Axis
		Fx		Mx		Fy		My		Fz		Mz
		+ (extrusion) − (Intrusion)		+ (distal rotation) − (mesial rotation)		+ (distal) − (Mesial)		+ (lingual root torque) //− (buccal root torque)		+ (lingual) − (Buccal)		+ (distal tipping) − (Mesial tipping)
Tooth Rotation		4.5° Mesial	4.5° Distal	4.5° Mesial	4.5° Distal	4.5° Mesial	4.5° Distal	4.5° Mesial	4.5° Distal	4.5° Mesial	4.5° Distal	4.5° Mesial	4.5° Distal
Group 1: “Rectangular Vertical”	VRecUp	−170	−70	7,640	−9,218	27	−151	−9,627	7,497	330	−255	2,662	−4,020
	VRecDOWN	−159	−40	6,761	−9,221	−5	−216	−7,546	7,704	266	−264	1,476	−5,402
Group 2: “Rectangular Horizontal”	HRecR	−165	3	6,560	−6,965	21	−136	−6,641	5,118	224	−176	1941	−4,645
	HRecL	−75	−79	3,857	−5,200	24	−86	−5,298	2,956	176	−93	1862	−2,438
	3Shape®Box	−177	52	5,680	−3,680	44	−67	−4,575	3,250	109	−78	1897	−2,274
	Bevelled	−118	−38	2,584	−6,827	22	−93	−1,083	3,911	37	−145	1,208	−2,392
Group 3: “Ellipsoid Vertical”	Vellipsoid	−147	−36	5,515	−5,245	73	−117	−5,948	5,880	193	−184	2,762	−3,434
Group 4: “Ellipsoid Horizontal”	Hellipsoid	−122	−9	4,850	−1956	54	−40	−4,578	1909	165	−63	2,527	−1,307
	HemiEllipR	−135	28	4,674	−3,351	56	−20	−3,378	3,002	110	−113	2,324	−945
	HemiEllipL	−170	23	7,861	−5,358	69	−116	−8,116	5,245	301	−184	3,357	−3,500
Group 5: “Other”	ElliPair	−98	−27	5,195	−8,456	29	−173	−5,233	6,520	184	−229	1,643	−4,424
	NoAtt	−65	−137	2,198	−1,582	64	−10	−2042	1970	67	−60	2,363	−96