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As described previously, the base of the extender mechanism was modeled by a four-bar vector loop (R2 + R3 - R4 - R1 = 0), and the other linkages could be calculated based on geometric relationships to the vectors in the initial vector loop. The fourbarpos.m MATLAB function was used to determine the angles of each of the vectors (ΘAΘ_A, ΘB Θ_B, ΘC Θ_C, ΘD Θ_D). From here, the appropriate vectors were split into their real and imaginary components,

ae^jΘ_A + be^jΘ_B - ce^jΘ_C - de^jΘ_D = 0

a(cosΘ_A + jsinΘ_A) + b(cosΘ_B + jsinΘ_B) - c(cosΘ_C + jsinΘ_C) - d(cosΘ_D + jsinΘ_D) = 0

then summed to determine the X and Y coordinate for points P1, P2, and P3. The results of the position analysis are shown in Figures C and D.

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