For the TE, the lower part of the implant was parallel and the lateral surface and axial surface had the same taper in the cervical region. TE10 in Fig. 4a showed a torque curve with a similar form to BL10 in Fig. 3 and had three kinds of areas. The torque curves for MK3 and MK4 in Fig. 4a had an area in which the torque finally rose suddenly after reaching its critical point and became moderate. This was distinguished from the tapered areas of BL and TE and assumed to be a platform area. MK4 had a gentle taper on the entire axial surface and platform. The platform area, shown in ④, was seen at the end of the torque curve in Fig. 5a, and its torque value was the maximum value among the nine kinds evaluated in this study. In past reports, MK3 was parallel, similar to ST, and had a platform, similar to MK4, and a platform area was seen in the last part of the torque curve. In MK3, the platform area followed the initial area and parallel area, although it presented a final torque value of 4.3 N · cm in the parallel area and then rose further to 10.7 N · cm in the platform area.

Removal torque

In the removal torque curve, the characteristics of the implant design were not clearly recognized, compared with the implant torque curve. In all implants, the torque rose suddenly immediately after removal was started and reached a peak value. The changes in torque from the peak value were classified into two types. For ST shown in Fig. 2b, the torque fell gently from the peak value. For BL, TE, MK3, and MK4 in Figs. 3b, 4b, and 5b, a sudden fall in torque was seen immediately after the peak value, and it then fell gently. Table 2 shows the maximal values for insertion torque value (IT) and RT obtained from the torque curves and the p values obtained by significance tests for RT and IT. The RT for six kinds of implants (BL8, 10, 12, TE10, MK3, MK4) was smaller than the corresponding IT, with statistical significance (p < 0.05), while the RT for ST6, 8, and 10 was almost the same as or slightly greater than the corresponding IT.

Torque rise rate

Table 3 shows the average torque rise obtained from the torque curve according to areas. The mean torque rise rate of the parallel area was the smallest at 0.36 N · cm/s and differed significantly from those of the other areas (p < 0.05). Specifically, the rates were 2.14, 2.33, and 2.65 N · cm/s for the initial area, tapered area, and platform area, respectively, and greater than those of the parallel area by 6–7 times, although significant differences were not recognized among the mean values of these three areas.