Table 8 Type synthesis process
| Â | Branch chain constraint line graph and dual DOF graph with couple | Redundant DOF graph | Corresponding branched chain structure |
|---|---|---|---|
Chains 1 |
|
| \( (RR\overline{\overline{\text{R}}} {\text{RR}})_{E} { - }\overline{\overline{\text{R}}} \) \( (R{\text{P}}\overline{\overline{\text{R}}} {\text{PR}})_{E} { - }\overline{\overline{\text{R}}} \) \( ({\text{P}}R\overline{\overline{\text{R}}} {\text{RP}})_{E} { - }\overline{\overline{\text{R}}} \) \( ({\text{RR}} {\overline{\text{R}}} {\overline{\text{R}}} {{\text{RR}}})_{{\text{E}}} { - } {\overline{\text{R}}}\) \( ({\text{RP}} {\overline{\text{R}}} {\overline{\text{R}}} {\text{PR}})_{{\text{E}}} { - } {\overline{\text{R}}} \) \( ({\text{PR}} {\overline{\text{R}}} {\overline{\text{R}}} {\text{RP}})_{{\text{E}}} { - } {\overline{\text{R}}}\) \( 5\overline{R} - \overline{R} \) \( ({\text{P}}R\overline{R} {\text{RP}})_{E} { - }\overline{\text{R}} \) \( (R{\text{P}}\overline{R} {\text{PR}})_{E} { - }\overline{\text{R}} \) \( ({\text{P}}RR\overline{\overline{\text{R}}} {\text{RR}})_{E} { - }\overline{\overline{\text{R}}} \) \( ({\text{P}}R{\text{P}}\overline{\overline{\text{R}}} {\text{PR}})_{E} { - }\overline{\overline{\text{R}}} \) \( ({\text{PRR}} {\overline{\text{R}}} {\overline{\text{R}}} {\text{RR}})_{{\text{E}}} { - } {\overline{\text{R}}}\) \( ({\text{PRP}} {\overline{\text{R}}} {\overline{\text{R}}} {\text{PR}})_{{\text{E}}} { - } {\overline{\text{R}}}\) \( {\text{P}}5\overline{R} - \overline{R} \) \( ({\text{P}}R{\text{P}}\overline{R} {\text{PR}})_{E} { - }\overline{\text{R}} \) |
Chains 2 |
| ||
Branch chain assembly requirements | The force constraints provided by the two branches need to be parallel in space The force constraints provided by each branch chain are perpendicular to the plane formed by the two couple constraints provided by the branch chain The rank of couple constraint is 2 | ||
