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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)