Robotic arm movement Trigonometric functions are used extensively in the design of industr...

Robotic arm movement Trigonometric functions are used extensively in the design of industrial robots. Suppose that a robot’s shoulder joint is motorized so that the angle θ increases at a constant rate of π/12 radian per second from an initial angle of θ = 0. Assume that the elbow joint is always kept straight and that the arm has a constant length of 153 centimeters, as shown in the figure.

EXERCISE

(a) Assume that h = 50 cm when θ = 0. Construct a table that lists the angle θ and the height h of the robotic hand every second while 0 ≤ θ ≤ π/2.

(b) Determine whether or not a constant increase in the angle θ produces a constant increase in the height of the hand.

(c) Find the total distance that the hand moves.