1) The document provides instructions on using the relative velocity method to solve multiple mechanics problems involving rotating links and blocks. 2) Examples are given to determine velocities of various blocks and points on rotating systems using velocity polygons, where the angular velocity of rotating links are given. 3) Diagrams are included with the examples to illustrate the use of the relative velocity method and construction of velocity polygons to solve for unknown velocities.

1. Determine the velocity of the block if link 2 if link 10 turns at 10 rad/sec clockwise. Locate all
centros.
(INSERT FIG.)
Example: RELATIVE VELOCITY METHOD
Determine the velocity of block 6 and 3 if link 2 rotates at 10 rad/sec clockwise. 𝐾𝑠 =
1
4
𝑠𝑖𝑧𝑒, 𝐾𝑣 = 40
𝑐𝑚
𝑠𝑒𝑐
.
(INSERT FIG.)
(INSERT FIG.)
Velocity Polygon
𝑉𝐴 = 2𝜔2 𝐴
= 10(8)
𝑉𝐴 = 80 𝑐𝑚/𝑠𝑒𝑐
Procedure:
1) Locate a convenient location for pole c and lay out 𝑐𝑎2 equal and parallel to 𝑉𝐴 on 2.
2) To find 𝑉𝐴 on 4, 𝑉𝐴 on 4 = 𝑉𝐴 on 2. Sliding velocity
(a) Lay our from 𝑎2 a line parallel to link 4 representing the sliding velocity of the block.
(b) From pole c, draw a line parallel to the direction line of the velocity of A on 4 which
is perpendicular to link 4. 𝑉𝐴 𝑜𝑛 4 = 𝑐𝑎4 𝑥 𝐾𝑣 = 1.35(40) = 54 𝑐𝑚/𝑠𝑒𝑐
3) To find 𝑉𝐵 ,
Points A on 4 and 3 are rotating about the same axis of rotation, the velocities
are proportional to its distances from 𝑆4, likewise, the length of the vector in the
velocity polygon is proportional to its distance from pole c. Therefore,
4) To find 𝑉𝐷 , 𝑉𝐷 = 𝑉𝐵 ; 𝑉𝐵𝐷
a) Lay out a line from pole a parallel to the direction line of the velocity of the block.
b) Draw a line perpendicular to BD which is the direction line of the velocity of B
relative to D.
c) Measure cd, 𝑉𝐷 = 𝑐𝑑 𝑥 𝐾𝑣 = 0.58(40) = 20 𝑐𝑚/𝑠𝑒𝑐
=
𝑉 𝐵 𝐷
𝐵𝐷
=
0.35(40)
28
= 0.50 𝑟𝑎𝑑/𝑠𝑒𝑐
Example: RELATIVE VELOCITY METHOD
Determine the velocity of point B and the point of contact between the two
gears if the angular velocity of crank 2 is 10 rad/sec and gear 5 roll on gear 3 𝑥 𝑣 = 10 𝑐𝑚/𝑠𝑒𝑐

2. (INSERT FIG.)
Direction line of Point 0 on 3 rotating about 𝑐2.
𝑉𝐴 = 𝑐2 𝑎 𝑥 𝜔2
𝑉𝐴 = 10(2)
𝑉𝐴 = 20 𝑐𝑚/𝑠𝑒𝑐.
(INSERT FIG.)
Velocity Polygon
𝑉𝐴 = 𝑉𝐵 𝑉𝐵𝐴
𝑉𝐵 = 𝑜𝑏 𝑥 𝐾𝑣
𝑉𝐵 = 1.6(10)
𝑉𝐵 = 16 𝑐𝑚/𝑠𝑒𝑐.
𝑉0 𝑜𝑛 3 = 𝑉0 𝑜𝑛 5 = 𝑉𝐴
= 4(10) = 40 𝑐𝑚/𝑠𝑒𝑐
Oa is equal and parallel to 𝑉𝐴
hao perpendicular to AB.
Cb perpendicular to 𝑐4 𝑏
Co perpendicular to 𝑐2 𝑜
If crank 2 rotates uniformly at 20 rad/sec, determine the velocity of block 6 and the angular
velocity of link 5 in rad/sec. 𝐾𝑠 = 4𝑐𝑚/𝑐𝑚.
(INSERT FIG.)
Crank 2 rotates counterclockwise with an angular speed of 30 rad/sec. Determine
𝑉𝐵, 𝑉𝐷, 𝑉𝐸, 𝑊3 , 𝑊4 𝑎𝑛𝑑 𝑊7. 𝐾𝑠 = 3 𝑐𝑚/𝑐𝑚.
(INSERT FIG.)
Determine the velocity of block 5 and 4 if crank 2 rotates at 10 rad/sec. 𝐾𝑆 = 2𝑐𝑚/𝑐𝑚.
(INSERT FiG.)