An elementary course of infinitesimal calculus . Fig. 130. * Viz. if BP=a, AP=b, L OAB = <p, the coordinates of P are«=acos0, y=baiiiip. 28—2 436 INFINITESIMAL CALCULUS. LCH. Ex. 2. An arm OQ revolves about one extremity 0; a barQP is hinged to it at Q; and P is constrained to move in astraight line passing through 0. It is required to find therelations between the velocities of the points P and Q. Thisarrangement is that of the crank and connecting rod of a steam-engine with a fixed cylinder. The instantaneous centre / is at the intersection of OQproduced with the perpendicular to the fixe
An elementary course of infinitesimal calculus . Fig. 130. * Viz. if BP=a, AP=b, L OAB = <p, the coordinates of P are«=acos0, y=baiiiip. 28—2 436 INFINITESIMAL CALCULUS. LCH. Ex. 2. An arm OQ revolves about one extremity 0; a barQP is hinged to it at Q; and P is constrained to move in astraight line passing through 0. It is required to find therelations between the velocities of the points P and Q. Thisarrangement is that of the crank and connecting rod of a steam-engine with a fixed cylinder. The instantaneous centre / is at the intersection of OQproduced with the perpendicular to the fixed straight line at Fig. 131. Hence the velocity of P is to that of Q as IP to IQ. Let PQ,produced if necessary, meet the perpendicular through 0 to theline of motion of P in the point E. Then if w be the angularvelocity of OQ, TP OR velocityof P = o).OGx^= co. 0^ x ^ = «,. (l). Ex. 3. In an engine with an oscillating cylinder, the pistonrod, being connected directly with the crank OQ, has its directionalways passing through a fixed point G (on the pivot line of thecylinder). The instantaneous axis is now at the intersection of OQproduced with the perpendicular to the piston rod at C. Hence,if ON be the perpendicular from 0 on GQ, produced if necessary,the velocity of the point of the rod which coincides with C is ^^ = o>.ON (2). ,.0Q.^- OQ 163] CUEVAT0EE. 437
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