Andreau differential stroke mechanism:

An Andreau differential stroke mechanism is illustrated in given fig. A & B are gears that mesh together and rotate in opposite sense. Determine the velocity of slider D while gear B rotates at 750 rpm. The dimensions are given in figure

Solution

Like a first step the configuration diagram is plotted with appropriate scale. Given fig it has been plotted along a scale 1: 5.

No. of links = 7

∴ No. of I.Cs = (7 (7 - 1))/2 = 21

                                      Table of I. Cs

I₁₂         I₁₃         I₁₄         I₁₅         I₁₆         I₁₇

            I₂₃         I₂₄         I₂₅         I₂₆         I₂₇

                        I₃₄         I₃₅         I₃₆         I₃₇

                                    I₄₅         I₄₆         I₄₇

                                                I₅₆         I₅₇

                                                            I₆₇

All the I. Cs need not be resolute to get needed answer. For finding velocity of piston D, I₅₇ is necessary that relates motion of link 5 along motion of link 7. First find I₂₄ which is point of intersection of lines joining I₂₃ with I₃₄ & I₂₅ with I₄₅. I₁₄ is pt of intersection of lines joining I₁₂ along I₂₄ & I₁₅ along I₄₅. I₄₇ is point of intersection of lines joining I₁₇ along I₁₄ and I₆₇ along I₄₆. I₅₇ is the point of intersection of lines joining I₄₇ along I₄₅ & I₁₅ along I₁₇. The velocity of piston D

V_D = ω× I₁₅ I₅₇

ω= (2 π× 750)/60

and I₁₅ I₅₇ = 100 mm (from given fig)