Round 18: Tossup 1

A formula used to calculate this quantity fails when applied to a variation of the “E-quintet” mechanism whose nodes are collinear. In mechanical design, “number synthesis” targets a specific value of this quantity. This quantity differs by one between “full” and “half” joints. This quantity for each element of a linkage is added up in the (10[1])Grübler–Kutzbach (10[3])criterion. (10[2])High values of this quantity are bounded by a system’s “operational (10[1])envelope,” which causes the mobility to be small if the system is overconstrained. (10[3])The surge, heave, and sway correspond to the translational components (10[1])of this quantity, (10[2])which are combined with pitch, yaw, (10[1])and roll (10[1]-5[1])to (-5[1])obtain a standard value of six (10[1])of this quantity (10[1])for a rigid body. (10[1]-5[1])For 10 points, name this quantity (10[1])that determines the number of physical parameters of a system. ■END■ (10[4]0[1])

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