To interpolate the 4th line of the given G-code, we need to calculate the sectional times (T1, T2, and T3) and the number of interpolation steps for each section. Given: Sampling period (Ts) = 7, 10[msec] = 0.007, -0.01 [sec] Acceleration (A) = Deceleration (D) = 250 [mm/sec] Feedrate (F) = 600 [mm/min] = 10 [mm/sec] i) Calculation of Sectional Times: We know that the trapezoidal feedrate profile has three sections: acceleration, cruise, and deceleration. The total distance traveled (D) can be calculated as: D = (F^2)/(2A) = (10^2)/(2250) = 0.02 [m] = 20 [mm] The total time (T) can be calculated as: T 2D F 20.02 10 = 0.004[min] = 0.24 [sec] Explanation: Sectional times can be calculated as follows: T1 = (F/A) = (10/250) = 0.04 [sec] T3 = T1 T2T-T1-T3 = 0.24 -0.04 -0.04 = 0.16 [sec] ii) Calcationof InterpolationSteps : The rounded segment durations at the sampling period (Ts) can be calculated as follows: Ta = round(T1/Ts) = round(0.04/0.007) = 6 [samples] Tc = round(T2/Ts) = round(0.16/0.007) = 23 [samples] Td = round(T3/Ts) = round(0.04/0.007) = 6 [samples] iii) Interpolation of X and Y Axis Reference Commands: To interpolate the X and Y axis reference commands, we can use the following equations: s(t) = 0.5At^2 (0 t Ta) s(t) = (0.5ATa^2) + (F*(t-Ta)) (Ta < t Ta+Tc) s(t) = D - (0.5D^2/A) + (F(t-Ta-Tc)) (Ta+Tc < t Ta+Tc+Td) v(t) = At (0 t Ta) v(t) = F (Ta < t Ta+Tc) v(t) = D - A(t-Ta-Tc) (Ta+Tc < t Ta+Tc+Td) Explanation: The initial values for the table can be filled as follows: k[0] = 0 s[0] = 0 v[0] = 0 x[0] = 0 y[0] = 0 t[0] = 0 Then, we can fill in the remaining values for each sample as follows: For acceleration section (0 t Ta): k[i] = it[i] = Ts x i s[i] = 0.5At[i] v[i] = A*t[i] x[i] = 0.5*s[i] y[i] = 0.6 + (0.5*s[i]/s[Ta])*0.6 For cruise section (Ta < t Ta+Tc): k[i] = Ta+i A CNC interpolator is designed to generate trapezoidal feedrate profiles at a constant sampling period of T=10[msec]. The acceleration and deceleration magnitudes have )=250[mm/sec]. Using this information, interpolate the 4th line (N4) of been set to A=D= the G-code given below. Sample k[] 0 1 2 3 4 N1 % Example in metric and starting from X0.0 Y0.0 N2 G71 G90 G17 G40 N3 S1000 N4 G01 X0.5 Y0.6 F600 (mm/min!) Absolute Time t [sec] Displacement s [mm] Feedrate s[mm/sec] X Axis Command X [mm] Y Axis Command y, [mm]