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Table 2. The configurations of parallel mechanism 3(rA)P(rA)

From: Constraint and Mobility Change Analysis of Rubik’s Cube-inspired Reconfigurable Joints and Corresponding Parallel Mechanisms

No. Equivalent configuration Configuration
1 3SPS 3(1,2)P(1,2)
2 3UPS 3(3,4,5)P(1,2)
3 3RPS 3(6)P(1,2)
4 3UPU 3(3,4,5)P(3,4,5)
5 3RPU 3(6)P(3,4,5)
6 3RPR 3(6)P(6)
7 2SPS-UPS 2(1,2)P(1,2)-(3,4,5)P(1,2)
8 2SPS-RPS 2(1,2)P(1,2)-(6)P(1,2)
9 2SPS-UPU 2(1,2)P(1,2)-(3,4,5)P(3,4,5)
10 2SPS-UPR 2(1,2)P(1,2)-(3,4,5)P(6)
11 2SPS-RPR 2(1,2)P(1,2)-(6)P(6)
12 2UPS-SPS 2(3,4,5)P(1,2)-(1,2)P(1,2)
13 2UPS-UPR 2(3,4,5)P(1,2)-(3,4,5)P(1,2)
14 2UPS-RPS 2(3,4,5)P(1,2)-(6)P(1,2)
15 2UPS-UPU 2(3,4,5)P(1,2)-(3,4,5)P(3,4,5)
16 2UPS-RPR 2(3,4,5)P(1,2)-(6)P(6)
17 2RPS-SPS 2(6)P(1,2)-(1,2)P(1,2)
18 2RPS-UPS 2(6)P(3,4,5)-(3,4,5)P(1,2)
19 2RPS-UPU 2(6)P(1,2)-(3,4,5)P(3,4,5)
20 2RPS-UPR 2(6)P(1,2)-(3,4,5)P(6)
21 2RPS-RPR 2(6)P(1,2)-(6)P(6)
22 2UPU-SPS 2(3,4,5)P(3,4,5)-(1,2)P(1,2)
23 2UPU-UPS 2(3,4,5)P(3,4,5)-(3,4,5)P(1,2)
24 2UPU-RPS 2(3,4,5)P(3,4,5)-(6)P(1,2)
25 2UPU-UPR 2(3,4,5)P(3,4,5)-(3,4,5)P(6)
26 2UPU-RPR 2(3,4,5)P(3,4,5)-(6)P(6)
27 2RPR-SPS 2(6)P(6)-(1,2)P(1,2)
28 2RPR-UPS 2(6)P(6)-(3,4,5)P(1,2)
29 2RPR-RPS 2(6)P(6)-(6)P(1,2)
30 2RPR-UPU 2(6)P(6)-(3,4,5)P(3,4,5)
31 2RPR-UPR 2(6)P(6)-(3,4,5)P(6)
32 SPS-UPS-RPS (1,2)P(1,2)-(3,4,5)P(1,2)-(6)P(1,2)
33 SPS-UPS-UPU (1,2)P(1,2)-(3,4,5)P(1,2)-(3,4,5)P(3,4,5)
34 SPS-UPS-UPR (1,2)P(1,2)-(3,4,5)P(1,2)-(3,4,5)P(6)
35 SPS-UPS-RPR (1,2)P(1,2)-(3,4,5)P(1,2)-(6)P(6)
36 SPS-RPS-UPU (1,2)P(1,2)-(6)P(1,2)-(3,4,5)P(3,4,5)
37 SPS-RPS-UPR (1,2)P(1,2)-(6)P(1,2)-(3,4,5)P(6)
38 SPS-RPS-RPR (1,2)P(1,2)-(6)P(1,2)-(6)P(6)
39 SPS-UPU-UPR (1,2)P(1,2)-(3,4,5)P(3,4,5)-(3,4,5)P(6)
40 SPS-UPU-RPR (1,2)P(1,2)-(3,4,5)P(3,4,5)-(6)P(6)
41 SPS-UPR-RPR (1,2)P(1,2)-(3,4,5)P(6)-(6)P(6)
42 UPS-RPS-UPU (3,4,5)P(1,2)-(6)P(1,2)-(3,4,5)P(3,4,5)
43 UPS-RPS-UPR (3,4,5)P(1,2)-(6)P(1,2)-(3,4,5)P(6)
44 UPS-RPS-RPR (3,4,5)P(1,2)-(6)P(1,2)-(6)P(6)
45 UPS-UPU-UPR (3,4,5)P(1,2)-(3,4,5)P(3,4,5)-(3,4,5)P(6)
46 UPS-UPU-RPR (3,4,5)P(1,2)-(3,4,5)P(3,4,5)-(6)P(6)
47 UPS-UPR-RPR (3,4,5)P(1,2)-(3,4,5)P(6)-(6)P(6)
48 RPS-UPU-UPR (6)P(1,2)-(3,4,5)P(3,4,5)-(3,4,5)P(6)
49 RPS-UPU-RPR (6)P(1,2)-(3,4,5)P(3,4,5)-(6)P(6)
50 RPS-UPR-RPR (6)P(1,2)-(3,4,5)P(6)-(6)P(6)
51 UPU-UPR-RPR (3,4,5)P(3,4,5)-(3,4,5)P(6)-(6)P(6)