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TableĀ 6 The second type PMs with closed loop unit

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

The second type PMs with closed loop unit
\( 2\left[ {(\text{RR}\overline{\overline{\text{R}}} \text{RR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {(\text{RP}\overline{\overline{\text{R}}} \text{PR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {(\text{PR}\overline{\overline{\text{R}}} \text{RP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {(\text{PP}\overline{\overline{\text{R}}} \text{PP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {5\overline{\text{R}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{\text{R}} } \right]{ - }2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {(\text{RP}\overline{\text{R}} \text{PR})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{\text{R}} } \right] - 2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {(\text{RP}\overline{\overline{\text{R}}} \text{PR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2{\text{UPR}} \)
\( 2\left[ {(\text{PR}\overline{\overline{\text{R}}} \text{RP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2{\text{UPR}} \)
\( 2\left[ {(\text{PP}\overline{\overline{\text{R}}} \text{PP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2{\text{UPR}} \)
\( 2\left[ {5\overline{\text{R}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{UPR}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{\text{R}} } \right]{ - }2{\text{UPR}} \)
\( 2\left[ {(\text{RP}\overline{\text{R}} \text{PR})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{\text{R}} } \right] - 2{\text{UPR}} \)
\( 2\left[ {(\text{RR}\overline{\overline{\text{R}}} \text{RR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2{\text{URP}} \)
\( 2\left[ {(\text{RP}\overline{\overline{\text{R}}} \text{PR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2{\text{URP}} \)
\( 2\left[ {(\text{PR}\overline{\overline{\text{R}}} \text{RP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2{\text{URP}} \)
\( 2\left[ {(\text{PP}\overline{\overline{\text{R}}} \text{PP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2{\text{URP}} \)
\( 2\left[ {5\overline{\text{R}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{URP}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{\text{R}} } \right]{ - }2{\text{URP}} \)
\( 2\left[ {(\text{RP}\overline{\text{R}} \text{PR})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{\text{R}} } \right] - 2{\text{URP}} \)
\( 2\left[ {(\text{RR}\overline{\overline{\text{R}}} \text{RR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {(\text{RP}\overline{\overline{\text{R}}} \text{PR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {(\text{PR}\overline{\overline{\text{R}}} \text{RP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {(\text{PP}\overline{\overline{\text{R}}} \text{PP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {5\overline{\text{R}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{\text{R}} } \right]{ - }2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {(\text{RR}\overline{\overline{\text{R}}} \text{RR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2\underline{\text{R} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {(\text{RP}\overline{\overline{\text{R}}} \text{PR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2\underline{\text{R} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {(\text{PR}\overline{\overline{\text{R}}} \text{RP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {(\text{PP}\overline{\overline{\text{R}}} \text{PP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {5\overline{\text{R}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{\text{R}} } \right]{ - }2\underline{\text{R} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {(\text{RP}\overline{\text{R}} \text{PR})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{\text{R}} } \right] - 2\underline{\text{R} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {(\text{RR}\overline{\overline{\text{R}}} \text{RR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2\underline{\text{R}} (P\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{RP}\overline{\overline{\text{R}}} \text{PR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2\underline{\text{R}} (\text{P}\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{PR}\overline{\overline{\text{R}}} \text{RP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} (P\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{PP}\overline{\overline{\text{R}}} \text{PP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} (\text{P}\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {5\overline{\text{R}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} (\text{P}\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{\text{R}} } \right]{ - }2\underline{\text{R}} (\text{P}\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{RP}\overline{\text{R}} \text{PR})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{\text{R}} } \right] - 2\underline{\text{R}} (\text{P}\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{RR}\overline{\overline{\text{R}}} \text{RR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2{\text{P}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{RP}\overline{\overline{\text{R}}} \text{PR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2{{\text{P}}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{PR}\overline{\overline{\text{R}}} \text{RP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2{\text{P}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{PP}\overline{\overline{\text{R}}} \text{PP})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right]{ - }2{\text{P}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {5\overline{\text{R}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{P}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{RP}\overline{\text{R}} \text{PR})_{\text{E}} - \overline{{\underline{\text{R} }}} \overline{\text{R}} } \right] - 2{\text{P}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{\text{R}} } \right]{ - }2{\text{P}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {{\text{P}} \, \overline{\text{R}} \, \overline{\text{U}} \,\overline{\text{R}}\, {\text{P}}} \right]{ - }2{\text{P}} \,\underline{R} \,(\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {\overline{\text{R}} \text{P}\overline{\text{U}} \text{P}\overline{\text{R}} } \right]{ - }2{\text{P}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{RR}\overline{\text{R}} \overline{\text{R}} \text{RR})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {(\text{PP}\overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {(\text{RRURR})_{\text{E}} } \right]{ - }2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {(\text{PP}\overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {{\text{P}} \, \overline{\text{R}} \, \overline{\text{U}} \, \overline{\text{R}} \, {\text{P}}} \right]{ - }2\overline{\text{U}} \overline{\text{R}} \, \overline{\text{R}} \)
\( 2\left[ {\overline{\text{R}} P\overline{\text{U}} P\overline{\text{R}} } \right]{ - }2\overline{\text{U}} \overline{\text{R}} \overline{\text{R}} \)
\( 2\left[ {(\text{RR}\overline{\overline{\text{R}}} \text{RR})_{\text{E}} - \underline{{\overline{{\overline{\text{R}} }} }} \underline{\text{R}} } \right] - 2{\text{UPR}} \)
\( 2\left[ {(\text{RR}\overline{\text{R}} \overline{\text{R}} \text{RR})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{UPR}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{UPR}} \)
\( 2\left[ {(\text{PP}\overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{UPR}} \)
\( 2\left[ {(\text{RRURR})_{\text{E}} } \right]{ - }2{\text{UPR}} \)
\( 2\left[ {(\text{PP}\overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{UPR}} \)
\( 2\left[ {{\text{P}} \,\overline{\text{R}}\, \overline{\text{U}} \,\overline{\text{R}}\, {\text{P}}} \right]{ - }2{\text{UPR}} \)
\( 2\left[ {\overline{\text{R}} \text{P}\overline{\text{U}} \text{P}\overline{\text{R}} } \right]{ - }2{\text{UPR}} \)
\( 2\left[ {(\text{RR}\overline{\text{R}} \overline{\text{R}} \text{RR})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{URP}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{URP}} \)
\( 2\left[ {(\text{PP}\overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{URP}} \)
\( 2\left[ {(\text{RRURR})_{\text{E}} } \right]{ - }2{\text{URP}} \)
\( 2\left[ {(\text{PP}\overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{URP}} \)
\( 2\left[ {{\text{P}} \,\overline{\text{R}}\, \overline{\text{U}} \,\overline{\text{R}}\, {\text{P}}} \right]{ - }2{\text{URP}} \)
\( 2\left[ {\overline{\text{R}} \text{P}\overline{\text{U}} \text{P}\overline{\text{R}} } \right]{ - }2{\text{URP}} \)
\( 2\left[ {(\text{RR}\overline{\text{R}} \overline{\text{R}} \text{RR})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {(PP\overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {(\text{RRURR})_{\text{E}} } \right]{ - }2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {(\text{PP}\overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {{\text{P}} \,\overline{\text{R}} \, \overline{\text{U}} \overline{\text{R}} \, {\text{P}}} \right]{ - }2\underline{R} \left( {\underline{R} RP} \right)_{E} \)
\( 2\left[ {\overline{\text{R}} P\overline{\text{U}} P\overline{\text{R}} } \right]{ - }2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {(\text{RP}\overline{\text{R}} \text{PR})_{\text{E}} - \overline{{\underline{\text{R}} }} \overline{{\underline{\text{R}} }} } \right] - 2\underline{\text{R}} \left( {\underline{\text{R}} \text{RP}} \right)_{\text{E}} \)
\( 2\left[ {(\text{RR}\overline{\text{R}} \, \overline{\text{R}} \text{RR})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {(\text{PP}\overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {(\text{RRURR})_{\text{E}} } \right]{ - }2\underline{\text{R} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {(\text{PP}\overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{{\text{R}} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {{\text{P}}{\overline{\text{R}}} {\overline{\text{U}}} {\overline{\text{R}}} {{\text{P}}}} \right]{ - }2{\underline{\text{R}}} \left( {{\underline{\text{R}}} {{\text{PR}}}} \right)_{{{\text{E}}}} \)
\( 2\left[ {\overline{\text{R}} \text{P}\overline{\text{U}} \text{P}\overline{\text{R}} } \right]{ - }2\underline{\text{R} } \left( {\underline{\text{R}} \text{PR}} \right)_{\text{E}} \)
\( 2\left[ {(\text{RR}\overline{\text{R}} \, \overline{\text{R}} \text{RR})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} (\text{P}\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \, \overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} (\text{P}\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{PP}\overline{\text{R}} \, \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} (P\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{RRURR})_{\text{E}} } \right]{ - }2\underline{\text{R}} (\text{P}\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {({\text{PP}} \overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2\underline{\text{R}} (\text{P}\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {{\text{P}} {\overline{\text{R}}} {\overline{\text{U}}} {\overline{\text{R}}} {{\text{P}}}} \right]{ - }2 {\underline{\text{R}}} ({{\text{P}}} {\underline{\text{RR}}})_{{{\text{E}}}}\)
\( 2\left[ {\overline{\text{R}} \text{P}\overline{\text{U}} \text{P}\overline{\text{R}} } \right]{ - }2\underline{\text{R}} (P\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{RR}\overline{\text{R}} \overline{\text{R}} \text{R}R)_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{P}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{PR}\overline{\text{R}} \overline{\text{R}} \text{RP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{P}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{PP}\overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{R} }} \underline{\text{R}} } \right]{ - }2{\text{P}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{RRURR})_{\text{E}} } \right]{ - }2{\text{P}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)
\( 2\left[ {(\text{PP}\overline{\text{R}} \overline{\text{R}} \text{PP})_{\text{E}} - \overline{{\underline{\text{R}} }} \underline{\text{R}} } \right]{ - }2{\text{P}}\underline{\text{R}} (\underline{\text{R}} \text{R})_{\text{E}} \)