The graph for x -componentas a function of timeis plotted is as shown in Figure 1.

The graph for y -component as a function of time is plotted is as shown in Figure 2.

The amplitude of sine and cosine function is 5, the frequency is 1 Hz, the period of the tip of a one-link robot is 1 s, the phase angle is 0 rad and the time shift of the one-link robot is 0 s.

Given:

The tip of a one-link robot is initially located at θ=0 attime t=0 s. The given figure is shown below,

Time taken for the robot to move form θ=0 to θ=2π rad is 1 s.

A one-link robot is length of 5 in.

Concept used:

Write the expression for the linear frequency.

  f=1T ....... (1)

Here, f is the linear frequency and T is the time period.

Write the expression for the angular frequency.

  ω=2πT ....... (2)

Here, ω is the angular frequency.

Write the expression for the time period.

  T=2πω ....... (3)

Write the expression for x -component at any time,

  x(t)=lcos(θ) ....... (4)

Here, x(t) is the expression for x -component at any time, l is the length of one-link robot, θ is the angle.

Write the expression for x -component at any time.

  y(t)=lsin(θ) ....... (5)

Here, y(t) is the expression for y -component at any time.

Write the expression for the time shift.

  t0=ϕω ....... (6)

Here, t0 is the expression for the time shift.

Calculation:

The one-link robot completes one revolution in 1 s.

Substitute 1 s for T in equation (2).

  ω=2π1 s=2π rad/s

Substitute 2π rad/s for ω in equation (3).

  T=2π2π s=1 s

Therefore, the period of the tip of a one-link robot is 1 s.

Substitute 1 s for T in equation (1).

  f=11 s=1 Hz

Therefore, the frequency is 1 Hz.

Since the one-link robot initially start form θ=0 and the phase angle is 0 rad.

Substitute ωt+ϕ for θ in equation (4).

  x(t)=lcos(ωt+ϕ) ....... (7)

Here, t is any given time and ϕ is the phase angle.

Substitute 5 in for l, 0 rad for ϕ and 2π rad/s for ω in equation (7).

  x(t)=(5)cos(( 2π)t+0)=5cos2πt

The plot for the x -component as a function of time is shown in Figure 1.

Substitute ωt+ϕ for θ in equation (5).

  y(t)=lsin(ωt+ϕ) ....... (8)

Substitute 5 in for l, 0 rad for ϕ and 2π rad/s for ω in equation (8).

  x(t)=(5)sin(( 2π)t+0)=5sin(2πt+0)=5sin(2πt)

The plot for the y -component as a function of time is shown in Figure 2.

Figure 2

Substitute 0 rad for ϕ and 2π rad/s for ω in equation (6).

  t0 =0 rad2π rad/s=0 s

Therefore, the time shift of the one-link robot is 0 s.

The amplitude of sine and cosine function is 5.

Conclusion:

Thus, the graph for x -component is plotted in Figure 1 and y -component as a function of time is plotted in Figure 2. The amplitude of sine and cosine function is 5, the frequency is 1 Hz, the period of the tip of a one-link robot is 1 s, the phase angle is 0 rad and the time shift of the one-link robot is 0 s.