Skip to main content

Table 8 Type synthesis process

From: A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

  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