### Table 2: Initial net activations for free choice.

### Table 3: Relations between cognitions for free choice.

### Table 2: Results on synthesis minimized PNs and free-choice PNs. ((*) silent events hidden before synthesis)

1998

"... In PAGE 32: ... Such an approach has been used in [47] to synthesize asynchronous circuits from CSP-like descriptions. Efficiency of PN synthesis Table2 describes the results of the application of our algorithms to the minimization of labeled Petri nets. The examples (taken from the set of standard benchmarks for asynchronous control circuits [34]) correspond to specifications of asynchronous circuits that have been produced manually by system designers.... ..."

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### Table 2. Free choices for 2-link SDCSC mechanism RBG and PF synthesis. PPs Equations Variables Free Choices M 6M-4 M+10 14 -5M

1997

Cited by 2

### Table 1. Enumeration of free choices for a two-link SDCSC mechanism for the PF with kinematic speci cation at the precision points. PPs Equations Variables Free Choices M 2M Z0;Z1;Z2;R1; 6 ? M

"... In PAGE 4: ... 1 = 1 + ? 1 2 = (( 2 + R1 ? 2) ? ( 1 + ? 1)) (10) 1 and 2 are the absolute joint angles of the unde ected con guration of the two springs whereas 1 and 2 are the orientation of the rst and second links in the rst con gu- ration of the mechanism. The virtual angular displacements, 1 and 2, can be expressed in terms of the virtual displacement, as h 1 2 i = @ 1 @ @ 2 @ = h 1 (R1 ? 1)i (11) By substituting the above equation into the virtual work equation, the input torque, TI can be obtained as TI( ) = ?(Fx @ZPx @ + Fy @ZPy @ + Mz @ @ ) = ?[A1 A2 A3 A4]2 4Z1x Z1y Z2x Z2y 3 5 ? R1Mz + K1( 1 + ? 1) +K2(( 2 ? 1) + (R1 ? 1) ? ( 2 ? 1))(R1 ? 1)(12) 4 KINETOSTATIC SYNTHESIS ProcedureBased on the kinetostatic synthesis equations developed in the last equation, Table1 and Table 2 summarize the 4 Copyright c... ..."

### Table 2. Enumeration of free choices for a two-link SDCSC mechanism for the PF with kinetostatic speci cation at the precision points. PPs Equations Variables Free Choices M 3M Z0;Z1;Z2;R1; 6 ? 2M

"... In PAGE 4: ... 1 = 1 + ? 1 2 = (( 2 + R1 ? 2) ? ( 1 + ? 1)) (10) 1 and 2 are the absolute joint angles of the unde ected con guration of the two springs whereas 1 and 2 are the orientation of the rst and second links in the rst con gu- ration of the mechanism. The virtual angular displacements, 1 and 2, can be expressed in terms of the virtual displacement, as h 1 2 i = @ 1 @ @ 2 @ = h 1 (R1 ? 1)i (11) By substituting the above equation into the virtual work equation, the input torque, TI can be obtained as TI( ) = ?(Fx @ZPx @ + Fy @ZPy @ + Mz @ @ ) = ?[A1 A2 A3 A4]2 4Z1x Z1y Z2x Z2y 3 5 ? R1Mz + K1( 1 + ? 1) +K2(( 2 ? 1) + (R1 ? 1) ? ( 2 ? 1))(R1 ? 1)(12) 4 KINETOSTATIC SYNTHESIS ProcedureBased on the kinetostatic synthesis equations developed in the last equation, Table 1 and Table2 summarize the 4 Copyright c... ..."

### Table 2: Area results (n03 non-free-choice STGs, n3f totals restricted to STGs synthetized by FCG).

"... In PAGE 7: ... 9.2 Area of the circuits Table2 compares the area results of several synthesis tools in- cluding our methodology. The first column depicts the number of markings for the benchmark, while the columns labeled SYN, FCG and S3C reports the area obtained by the synthesis method- ologiesdevelopedat Stanford [1], Aizu [8], and our methodology.... ..."

### Table 5: Area results comparison ( non-free-choice STGs)((1)totals for STGs synthetized by SYN, (2)totals for STGs synthetized by FORCAGE).

"... In PAGE 39: ... 10.2 Area of the Circuits Table5 compares the area results of several synthesis tools including our methodology. The rst column depicts the number of markings for the benchmark, while the columns labeled SYN, FORCAGE and our tool reports the area obtained by the synthesis methodologies developed at Stanford [1], Aizu [12], and our methodology.... ..."

### Table 2. Enumeration of free choices for a 2-link SDCSC mechanism for the RBG and PF problems for increasing numbers of precision points. RBG Problem PG Problem

1997

"... In PAGE 9: ...9). Table2 enumerates the number of equations, variables and free choices for 2 M 6 precision points for the 2-link SDCSC mechanism. For three precision points, the loop closure equations in terms of the mechanism parameters can be obtained by evaluating Eqn.... In PAGE 10: ...where P1; P2; P3 are the speci ed absolute positions of the end -e ector at the three precision points. As seen in Table2 , in the PG problem for 3 precision points, we have 9 scalar unknowns (Z0; Z1; Z2; R1; 2; 3) and 6 scalar equations yielding a total of 3 free choices. In the RBG problem, the input link rotation angles ( 2; 3) are no longer unknowns since they can be calculated using the orientation equation (Eqn.... ..."

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