PROBLEM 4-18c Statement: Given: Scale Figure P4-5c to obtain dimensions for the problem. Find and plot the position of any one piston as a function of crank AB as it rotates through one revolution. Once one piston's motion is defined, find the motions of the other two pistons and their phase relationship to the first piston. Measured link lengths: Solution: Crank length, AB a =4.8-mm b = 17.6 mm c:=0.mm Piston-rod length, BC, BD, and BE Offset See Figure P4-5c and Mathcad file P0418c. 1. Let pistons 1, 2, and 3 be at C, D, and E, respectively. 2. Solve first for piston 1 (link 6). Establish e, as a range variable: 821 0 deg, 2.deg. 360 deg 3. Determine 0, and d using equations 4.16 and 4.17. 3121)asin a-sin +I b d (21)=a.cos (21)-b.cos(8 31 (21)) 4. For each piston (slider) the crank angle is measured counter-clock-wise from the centerline of the piston, which goes through the point A in all cases. Thus, when the crank angle for piston 1 is 0 deg, it is 120 deg for piston 2 and 240 deg for piston 3. Thus, the crank angles for pistons 2 and 3 are 22(21) +120.deg 21 23(21) 21+ 240. deg 5. Determine 8, and d for pistons 2 and 3. a.sin( 22(21)) 32(21)= (921))-)+* d2(021)=a.cos ( 22 (021)) - b.cos (8 32 (021)) a.sin( 32(21)) 33(21): =asin b (33 d3(021)=a-cos ( 23 (21)) - b.cos (8 33 (821)) 6. Plot the piston displacements as a function of crank angle (referenced to line AC(see next page). 22 Piston Displacement (1, 2, and 3) 24 d1 21) mm 20 21 mm d 3 21 Mini 20 18 16 Piston displacement, m 14. 12 60 120 180 240 300 360 021 deg Piston 1 crank angle, deg. The solid line is piston 1, the dotted line is piston 2, and the dashed line is piston 3.