You are to program a robotic arm on an assembly line to move in the xy -plane. I

Question

You are to program a robotic arm on an assembly line to move in the xy-plane. Its first displacement is A? ; its second displacement is B? , of magnitude 6.37cm and direction 62.8? measured in the sense from the +x-axis toward the -y-axis. The resultant C? =A? +B?  of the two displacements should also have a magnitude of 6.37cm , but a direction 22.3? measured in the sense from the +x-axis toward the +y-axis.

a) Find the component Ax of A? .

b) Find the component Ay of A? .

c) Find the magnitude of A? .

d) Find the direction of A?  measured in the sense from +x - axis toward the +y - axis.

Explanation / Answer

A=C-B

A=6.37(COS22.3I +SIN23.3J)-[6.37(C0S(-62.8)I+SIN(-62.8)J)]

A=2.98I+8.08J

the component Ax of A? .=2.98

the component Ay of A? .=8.08

the magnitude of A? .=8.61

the direction of A?  measured in the sense from +x - axis toward the +y - axis.=ARCTAN Ay/Ax =69.76DEGREE

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