Non-iterative geometric approach for inverse kinematics of redundant lead-module in a radiosurgical snake-like robot

Table 2 Computation of virtual points in the proposed geometric IK model

Id	Target position (mm)			VP_C1 (mm)			VP_M (mm)			VP_C2 (mm)
Id	X	Y	Z	X	Y	Z	X	Y	Z	X	Y	Z
1^a	35.895	47.082	22.319	6.669	8.477	0
2^a	11.162	32.623	−47.650	3.561	10.408	0
3^a	−20.562	−35.615	10.237	5.500	9.526	0
4^a	−46.787	−33.441	−25.663	−8.949	−6.396	0
5^a	−17.643	34.559	45.263	−5.002	9.797	0
6	−23.033	44.716	16.960	−10.987	−0.538	0	−63.289	−3.097	8.924	−56.205	5.318	8.924
7	95.978	20.201	−7.583	6.804	8.643	0	39.576	50.276	−3.795	49.282	45.100	−3.795
8	−70.092	96.494	−13.310	−9.188	6.049	0	−53.205	35.030	−6.652	−56.120	45.637	−6.652
9	−40.512	21.263	−13.329	−9.490	−5.562	0	−54.933	−32.193	−6.889	−52.420	−21.484	−6.889
10	−102.447	−12.848	−7.496	−8.003	−7.5469	0	−46.553	−43.900	−3.751	−56.168	−38.558	−3.751
11	4.644	28.145	10.142	−10.124	4.302	0	−58.757	24.971	5.423	−47.770	25.521	5.423
12	−42.313	−35.407	21.584	−8.365	−7.142	0	−48.417	−41.340	−6.942	−47.039	−30.429	−6.942
13	124.266	−26.778	−10.907	10.932	−1.220	0	63.446	−7.083	−5.449	73.9107	−10.4715	−5.449
14	52.552	−106.386	11.648	8.161	−7.375	0	47.335	−42.777	5.823	48.234	−53.740	5.823
15	29.670	104.466	19.317	−2.813	10.634	0	−16.167	61.129	9.677	−8.174	68.686	9.677

ISSN: 1475-925X