Question

the hand-operated shear shown in the Figure, use the relative velocity method to determine the angular velocity of the handle required to have the blade cut through the metal at a rate of 3 mm/s. Also determine the linear velocity of point X. a) Graphically present the velocity diagrams with all the angles and dimensions shown (20 marks) b) Analytically determine the results using trigonometric functions (15 marks) 0 mm 100 mm 60 mm

Answer 1

Given hand operated Shear has rate of 3 m m/s (a) Graphically determining linear velocity with the help of velocity diagrams The kinetic diagram of question is velocity at B is V_ B = V_C + V_ B/C where V_B , V_C are absolute velocities & V_B/C is velocity of B with respect to C And V_X = V_B + V_X/B Draw the velocity diagram All dimensions are , drawn to scale Measure V_B length: V_B = 3. 19 m/s V_B made angle of 25^degrees Therefore W_B = V_B/r_B = 3. 19/60 = 0. 053 rad/s c. cw Measure V_X length: V_X = 13. 32 m/s It made 51. 66^degree south - west Rightarrow velocity of X is V_X = 13. 32 m/s with 51. 6^degree s - w angle (b) Analytically determining the velocity with the help of trigonometric functions Crank was rotating counter clockwise Now draw kinetic diagram of the machine we know < D = 180 - 90 - 25 = 65^degree From delta , rectangular we found C D = B C . sin beta + A B times cos 65 Because from delta C B O , delta o' B D