Question

5. In the linkage shown, link 2 is rotating in the direction of CW at the constant angular velocity of 100 rad/s. In the position shown, determine the acceleration of joint C, and the angular acceleration of link 3 by using graphical approach. The link lengths of AB and BC are 60 mm and 200 mm, respectively. Link AB and slider guide are horizontal in the given position (20 points). 120 mm

Answer 1

Given W, = 100 rad/s CW 4,500 mm/s 24.50 7.5 6000 mms velocity polygon 63 600,000 mm is? Velo City Poly gon

velocity analysis VB - Voz + VBg leg VB 3 & VB2 VB2 = VAR + VB2 / A2 VAZ ²0 Therefore Vez & WB 3 kg = VAR + VB2 / A2 W, = 100 rad's Cw VB2/A2 = Wz X8BIA (+ to 8 BLA) perpendicular to 8 BA VBalan - 100 sad/s x60mm VBalAz = 6ooommis Voz 183 = W3x8c/B (perpendiculas to 80/B) Veyrou paralled to the ground graphically with a velocity Polygon. From the polygon Vez/B3 = 7,500mmis Veulby = 4,500 mm/s Vc 3/B3 = W3 x 8 c/B Ve 3/B31 1W31- 18oBl

W3 = 7,500 200 W3 = 37.5 radls from the directions given the position and velocity polygons W2 = 0.12 rad/S CW Accele sation analysis a B₂ = a Br - A B2/A2 aGz = acu - aculoh = a Bataca/B3 asculpy ta culbu = a Bel Azt a & Bala2 ta 23/B3 tat63/B3 row a B2/A2 = Wzx (W z XOBIA) a BelA2 = { W21².18BIAI a Balaz - 100² x 60 in a B2/t2 = 600,000 mm ls² the direction of Belar a Bz/A, = 0 (since link 2 rotates at a constant speed (de :o))

a 63/B2 - W₂ x (W₂ x 8 c1B). la 8/B₂ 1 = 1W 317 18cpl a cz1 B3 & 3752x200 asca (B3 = 281,000 mm/s² in the direction of 8C1B a & cz /B2 - az X8cIB latca (B21 - 123 1.180/B1 (t to 80/B). (perpendicular to rols) at 63/B3 = Kal. lrc/Bl parallel to ground a culou - doy solve the equation a culou ta culou- as Belart at B2 / Az + a 23/B3 t ta c3/B3 graphically with an acceleration polygon from the acceleration polygon a C31B2 = 211,000 mm ls 2 aculou = acu = 248,000 mm /s2

lat 63/B31 18c/Bl - 211,000 200 Iz & 1060 rad/s2 To determine the direction of da determine the direction that rolls must be robated to be parallel ko a'Bate at ca / B3 This direction is clearly counter - Clockwise from the acceleration polygon lacul - 248,000mm Is? The acceleration of joint c is ach = 248,000 mm ls² The angular acceleration of link 3 d3 - 1060 radls2