Research Article

IBOA-Based Optimization of Cross-Sectional Dimension of Rods for a 3-RRR PPM to Minimize Energy Consumption

Table 1

Parameters of dimension, kinematics, and dynamics for the 3-RRR PPM (where i = 1, 2, 3).

MeaningSymbol

Distance between hinge axes A1 and A2a
Distance between hinge axes A2 and A3b
Distance between hinge axes A3 and A1c
Distance between hinge axes C1 and C2d
Distance between hinge axes C2 and C3e
Distance between hinge axes C3 and C1f
Lengths of the active rods AiBili
Length of the passive rod BiCili+3
Global coordinates of the points Ai(xAi, yAi)
Global coordinates of the points Bi(xBi, yBi)
Global coordinates of the points Ci(xCi, yCi)
Local coordinates of the points Ci(xCi′, yCi′)
Global coordinate of the central point G7 of the moving platform(x, y)
Global coordinates of the points Gi(xGi, yGi)
Global coordinates of the points G(i+3)(xG(i+3),yG (i+3))
Orientation angle of the moving platformΘ
Rotation angle of the active rod AiBiθi
Angular velocities of the active rod AiBiωi
Rotation angle of the passive rod BiCiθi+3
Angular acceleration of the active rod AiBiαGi
Angular acceleration of the passive rod BiCiαG (i+3)
Angular acceleration of the moving platformαG7
Acceleration of the central points Gi of the active rod AiBiaGi
Acceleration of the central points G(i+3) of the passive rod BiCiaG(i+3)
Acceleration of the central point G7 of the moving platformaG7
Masses of the active rod AiBimGi
Masses of the passive rod BiCimG(i+3)
Masses of the moving platformmG7
The x-direction inertia forces of the active rod AiBiFGix
The y-direction inertia forces of the active rod AiBiFGiy
The x-direction inertia forces of the passive rod BiCiFG(i+3)x
The y-direction inertia forces of the passive rod BiCiFG(i+3)y
The x-direction inertia forces of the moving platformFG7x
The y-direction inertia forces of the moving platformFG7y
Rotary inertia round the centroidal axis of the active rod AiBiJGi
Rotary inertia round the centroidal axis of the passive rod BiCiJG (i+3)
Rotary inertia round the centroidal axis of the moving platformJG7
Moment of inertia of the active rod AiBiMGi
Moment of inertia of the passive rod BiCiMG(i+3)
Moment of inertia of the moving platformMG7
The x-direction external force of the moving platformFex
The y-direction external force of the moving platformFey
External moment of the moving platformMe
The x-direction internal forces at the point BiFBix
The y-direction internal forces at the point BiFBiy
The x-direction internal forces at the point CiFCix
The y-direction internal forces at the point CiFCiy
Driving moments of the active rod AiBiτi