Semi-Automatic Robotic Arm Cantilever Analysis

🔧 System Parameters

Beam Length (L)

Self-weight (w)

N/m

End-effector Load (P)

Step 1: Calculate Reaction Forces ▼

Sum of vertical forces (↑ positive):
ΣFy = 0: Ry - w×L - P = 0
Ry = --

Sum of moments about base (↺ positive):
ΣM = 0: M_base - w×L×(L/2) - P×L = 0
M_base = --

Results:
Vertical Reaction: -- N
Base Moment: -- N·m

Step 2: Construct Shear Force Diagram ▼

Shear Force Equation (0 ≤ x ≤ L):
V(x) = -(wL + P) + w×x
V(x) = --- + --×x

Key Points:
At x = 0: V = -- N
At x = L: V = -- N
Max |Shear|: -- N

Step 3: Construct Bending Moment Diagram ▼

Bending Moment Equation (parabolic):
M(x) = -M_base + Ry×x - w×x²/2
M(x) = --- + --×x - --×x²

Key Points:
At x = 0: M = -- N·m
At x = L: M = -- N·m
Max |Moment|: -- N·m

Step 4: Critical Sections & Design Analysis ▼

Critical Point Analysis:
dM/dx = V(x) = 0 → x = Ry/w = -- mm
Note: For cantilever beams with downward loads, max moment occurs at support

Design Critical Values:
Max Shear: -- N at x = 0
Max Moment: -- N·m at x = 0
Safety Factor: -- (based on 250 MPa steel)

--mm

--kN·m

--N

For cantilever beams, maximum shear and moment occur at the fixed support. This determines the critical design section.

Tip Deflection: -- mm

L/Deflection Ratio: --

Based on analysis results, design recommendations will appear here.

Recommended: --