A New Methodology for Type Synthesis of Planar Linkages for Exoskeletons up to Five Angular Outputs
Abstract
:1. Introduction
2. Design Basics
- Type of human limb (lower limb, upper limb, or finger);
- Type of required motion;
- Number of human joints that are required to be rehabilitated and their trajectory;
- The available workspace for exoskeleton fixation;
- The ability of patient to carry the proposed mechanism.
3. Modified Graph Theory
- Ground link (1) is denoted as a square.
- The output link (4) is denoted as a hollow circle.
- Other links (2, 3) are denoted as vertices.
- The connection between the ground link and output link is denoted by a curved edge (d).
- Other joints are denoted as solid edges (a, b, c) as shown in Figure 1c.
4. Type Synthesis
4.1. Parallel Connection Method
- All angular output links should be represented usually at the right of the graph.
- Adding the RRR dyad starts from the last presented angular output link (including two links and three revolute joints).
- The first additional link is located directly above the current output link to represent the ‘newer angular output’. This link is represented as a hollow circle. Therefore, all angular outputs are located in parallel arrangement as shown in Figure 2.
- The second additional link is located at the left of the new angular output link. This link is denoted by ‘distributive link’.
- Joints between the previous output, newer output, and distributive links are represented by solid edges (i, j). In other words, angular outputs are presented vertically above each other.
- The last revolute joint (k) has some alternatives to connect the distributive link with other links, excluding the connections that produce rigid sub-chains. These alternatives generate the available topological graphs that can achieve the required number of angular output motions.
4.2. Series Connection Method
- One of the linkage configurations, with a specific number of angular outputs, is selected as illustrated in Figure 3a. The selected configuration has a latest RRR dyad that contains angular output ‘Ni’, link ‘Ci’, which is denoted as ‘cut link’, and revolute joints namely: e, f, and h.
- Starting from the cut link, ‘Ci’, joint ‘h’ is deleted and reconnected directly with the newer angular output ‘Ni+1’ which is located directly above the present cut link ‘Ci’ as shown in Figure 3b.
- The second additional link,’Ci+1’, is located at the left of new angular output ‘Ni+1’.
- The joint between the newer output ‘Ni+1’ and its adjacent cut link ‘Ci+1’ is represented by a solid edge ‘R1’. In other words, angular outputs are presented diagonally.
- The remaining two revolute joints (R2, R3) have some alternatives to connect newer output and its adjacent cut link with original links in the linkage graph. That produces some available topological graphs that can achieve the required number of angular output motions, noting that some connections that produce rigid sub-chains should be excluded.
- Additional angular output can be obtained by repeating steps 2–5 so that all angular outputs are located in stepped series arrangement as shown in Figure 3.
4.3. Generation of Two Angular Outputs Using Parallel Connection
- First angular output link is represented at the right of the graph (link-4).
- Adding RRR dyad starts from link-4 (including two additional links: 5, 6).
- Link-5 is located directly above link-4 to represent the second angular output link as shown in Figure 4b.
- The distributive link-6 is located at the left of link-5 as shown in Figure 4b.
- Joints between links (4, 5 and 6) are represented by solid edges (e, f) as shown in Figure 4b.
- The last revolute joint has three alternatives to connect distributive link-6 with other links (joints g, h, i) excluding the connections that produce rigid sub-chains. These alternatives generate three available topological graphs that can achieve two angular output motions as shown in Figure 4c.
- Linkage diagrams, shown in Figure 4d, can be obtained from their corresponding topological graphs as illustrated in Section 4.4.
4.4. Sketching of Linkage Diagrams
- The original four-bar linkage is sketched containing two fixed pivots, binary links (2, 3, 4), and four revolute joints (a, b, c, d).
- According to topology ‘T1’, link-1 is connected with three links (2, 4, 6). Therefore, a third pivot is added which is connected with a binary link-6 by a revolute joint ‘g’.
- According to topology ‘T1’, link-4 is connected with three links (1, 3, 5). Therefore, link-4 is converted into a ternary link which is connected with a binary link-5 by a revolute joint ‘e’.
- Two binary links (5 and 6) are connected by a revolute joint ‘f’.
5. Generation of Multiple Angular Outputs
5.1. Generation of Three Angular Outputs Using Parallel Connection
- The existing angular output links are represented at the right of the graph (links 4 and 5) as shown in Figure 5a.
- Adding the RRR dyad starts from link-5 (including two additional links: 7, 8).
- Link-7 is located directly above link-5 as a third angular output link as shown in Figure 5b.
- The distributive link-8 is located at the left of link-7.
- Joints between links (5, 7 and 8) are represented by solid edges (j, k) as shown in Figure 5b.
- The last revolute joint, l, has five alternatives to connect distributive link-8 with other links in the original linkage graph, excluding the connections that produce rigid sub-chains. These alternatives generate five available eight-bar topological graphs that can achieve three angular output motions as shown in Figure 5c.
- Linkage diagrams can be constructed from their corresponding topological graphs as illustrated in Section 4.4. Some of these linkage diagrams are shown in Figure 5d.
5.2. Generation of Three Angular Outputs Using Series Connection
- Link ‘7’ is added directly above the current cut link ‘6’ to present the newer angular output as a hollow circle as illustrated in Figure 6b.
- Joint ‘k’ is deleted and reconnected directly with the newer angular output ‘7’.
- Link-8 is added at the left of the new angular output as shown in Figure 6b.
- The joint between the newer output ‘7’ and its adjacent cut link ‘8’ is represented by solid edge ‘R1’.
- The remaining two revolute joints (R2, R3) have some alternatives to connect newer output and its adjacent cut link with other links, excluding the connections that produce rigid sub-chains. These alternatives generate the available topological graphs that can achieve the required number of angular output motions as shown in Figure 6c.
- Linkage diagrams can be established from their corresponding topological graphs as illustrated in Section 4.4.
6. Results
- ▪
- A total of three six-bar linkages with up to two angular outputs, illustrated in Figure 3.
- ▪
- A total of 15 eight-bar linkages with up to three angular outputs using parallel connection, illustrated in Figure A1 (given in Appendix A).
- ▪
- A total of 16 ten-bar linkages with up to three angular outputs using series connection, illustrated in Figure 6c.
- ▪
- A total of 105 ten-bar linkages with up to four angular outputs using parallel connection, illustrated in Figure A2 (given in Appendix A).
- ▪
- A total of 18 (out of 576) ten-bar linkages with up to four angular outputs using series connection, illustrated in Figure A3 (given in Appendix A).
- ▪
- A total of 21 (out of 945) twelve-bar linkages with up to five angular outputs using parallel connection, illustrated in Figure A4 (given in Appendix A).
6.1. Example-1
6.2. Example-2
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
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No. of Angular Outputs | No. of Generated Linkages | No. of Links | No. of Joints | Connection Method |
---|---|---|---|---|
2 | 3 | 6 | 7 | Parallel |
3 | 15 | 8 | 10 | Parallel |
3 | 16 | 8 | 10 | Series |
4 | 105 | 10 | 13 | Parallel |
4 | 576 | 10 | 13 | Series |
5 | 945 | 12 | 16 | Parallel |
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Helal, M.; Alghtani, A.H.; Hu, J.W.; Eleashy, H. A New Methodology for Type Synthesis of Planar Linkages for Exoskeletons up to Five Angular Outputs. Appl. Sci. 2022, 12, 2238. https://doi.org/10.3390/app12042238
Helal M, Alghtani AH, Hu JW, Eleashy H. A New Methodology for Type Synthesis of Planar Linkages for Exoskeletons up to Five Angular Outputs. Applied Sciences. 2022; 12(4):2238. https://doi.org/10.3390/app12042238
Chicago/Turabian StyleHelal, Mahmoud, Abdulaziz H. Alghtani, Jong Wan Hu, and Hasan Eleashy. 2022. "A New Methodology for Type Synthesis of Planar Linkages for Exoskeletons up to Five Angular Outputs" Applied Sciences 12, no. 4: 2238. https://doi.org/10.3390/app12042238
APA StyleHelal, M., Alghtani, A. H., Hu, J. W., & Eleashy, H. (2022). A New Methodology for Type Synthesis of Planar Linkages for Exoskeletons up to Five Angular Outputs. Applied Sciences, 12(4), 2238. https://doi.org/10.3390/app12042238