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TableĀ 9 Types of symmetric mechanisms

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

Some 2T1R parallel mechanism representatives
\( 2\left[ {(R{\text{P}}\overline{\overline{\text{R}}} {\text{PR}})_{E} { - }\overline{\overline{\text{R}}} } \right] \) \( 2\left[ {({\text{P}}RR\overline{\overline{\text{R}}} {\text{RR}})_{E} { - }\overline{\overline{\text{R}}} } \right] \)
\( 2\left[ {({\text{P}}R\overline{\overline{\text{R}}} {\text{RP}})_{E} { - }\overline{\overline{\text{R}}} } \right] \) \( 2\left[ {({\text{P}}R{\text{P}}\overline{R} {\text{PR}})_{E} { - }\overline{\text{R}} } \right] \)
\( 2\left[ {5\overline{R} - \overline{R} } \right] \) \( 2\left[ {({\text{RR}} {\overline{\text{R}}} {\overline{\text{R}}} {\text{RR}})_{{\text{E}}} { - } {\overline{\text{R}}} } \right] \)
\( 2\left[ {({\text{P}}R\overline{R} {\text{RP}})_{E} { - }\overline{\text{R}} } \right] \) \( 2\left[ {(R{\text{P}} \, \overline{\text{R}} \, \overline{\text{R}} \, {\text{PR}})_{E} { - }\overline{\text{R}} } \right] \)
\( 2\left[ {(R{\text{P}}\overline{R} {\text{PR}})_{E} { - }\overline{\text{R}} } \right] \)\( 2\left[ {({\text{P}} \,R{\text{P}} \,\overline{\text{R}} \, \overline{\text{R}} \, {\text{PR}})_{E} { - }\overline{\text{R}} } \right] \) \( 2\left[ {({\text{P}} \, R \, \overline{\text{R}} \, \overline{\text{R}} \, {\text{RP}})_{E} { - }\overline{\text{R}} } \right] \)
\( 2\left[ {(RR\overline{\overline{R}} RR)_{E} - \overline{\overline{R}} } \right] \) \( 2\left[ {{\text{P}}5\overline{R} - \overline{R} } \right] \)
\( 2\left[ {({\text{P}} \, RR \,\overline{\text{R}} \, \overline{\text{R}} \, {\text{RR}})_{E} { - }\overline{\text{R}} } \right] \) \( 2\left[ {({\text{P}}R{\text{P}}\overline{\overline{\text{R}}} {\text{PR}})_{E} { - }\overline{\overline{\text{R}}} } \right] \)