Chapter 4, Problem 1P

To determine

To draw:

The position vector, x and y components of tip of one link robot and the representation in rectangular and polar form.

Answer to Problem 1P

The position vector is,

Its coordinates are, $\left(x,y\right)=\left(6,10.39\right)$.

The vector representation in rectangular form is in, and in polar form is in.

Explanation of Solution

Given Information:

Length of one link robot is 12 inches and its direction is $60°$.

Calculation:

The length and direction are given,

  $\begin{array}{l}P=12\text{ in}\\ \theta =60°\end{array}$

So,

  $\begin{array}{c}{P}_x=P\cos \theta \\ =12\cos \left(60°\right)\\ =6\text{ in}\\ P_y=P\sin \theta \\ =12\sin \left(60°\right)\\ =10.39\text{ in}\end{array}$

The position vector,

The coordinates,

  $\begin{array}{l}\left(x,y\right)=\left(P_x,P_y\right)\\ =\left(6,10.39\right)\end{array}$

The vector in rectangular form,

In polar form,

Conclusion:

The position vector is,

Its coordinates are, $\left(x,y\right)=\left(6,10.39\right)$.

The vector representation in rectangular form is in, and in polar form is in.