Mechanism Design Skill
Purpose
The Mechanism Design skill provides capabilities for mechanism kinematics, dynamics, and motion analysis, enabling systematic design and optimization of mechanical motion systems.
Capabilities
- Linkage synthesis and analysis
- Cam profile design
- Gear train design and analysis
- Kinematic simulation
- Dynamic force analysis
- Motion optimization
- ADAMS/RecurDyn integration
- Mechanism specification documentation
Usage Guidelines
Kinematic Analysis
Degrees of Freedom
Gruebler's Equation (planar):
DOF = 3(n-1) - 2j1 - j2
Where:
n = number of links (including ground)
j1 = number of full joints (pin, slider)
j2 = number of half joints (cam, gear)
DOF = 1: Constrained mechanism
DOF = 0: Structure
DOF < 0: Over-constrained
Common Mechanisms
| Mechanism | Links | Joints | DOF | Application | |-----------|-------|--------|-----|-------------| | Four-bar | 4 | 4 pins | 1 | Motion generation | | Slider-crank | 4 | 3 pins + 1 slider | 1 | Reciprocating motion | | Scotch yoke | 4 | 2 pins + 2 sliders | 1 | Exact sinusoidal | | Quick return | 4 | 3 pins + 1 slider | 1 | Unequal stroke times | | Geneva | 2 | Cam joint | Intermittent | Indexing |
Linkage Design
Four-Bar Linkage Types
Grashof criterion:
s + l <= p + q
Where:
s = shortest link
l = longest link
p, q = intermediate links
If satisfied: At least one link can rotate fully
Types:
- Crank-rocker: Shortest link is crank
- Double-crank: Shortest link is ground
- Double-rocker: No full rotation
Position Analysis
Loop closure equation:
r2*e^(i*theta2) + r3*e^(i*theta3) - r4*e^(i*theta4) - r1 = 0
Solve for theta3, theta4 given theta2 (input)
Velocity:
omega3 = omega2 * r2 * sin(theta4-theta2) / (r3 * sin(theta4-theta3))
Transmission Angle
mu = angle between coupler and output link
Ideal: mu = 90 degrees
Acceptable: 40 < mu < 140 degrees
Poor: mu < 30 or mu > 150 degrees
Cam Design
Cam Profile Types
| Type | Motion | Application | |------|--------|-------------| | Plate cam | Translating or oscillating follower | High speed | | Cylindrical cam | Oscillating follower | Indexing | | Face cam | Translating follower | Compact | | Globoidal cam | Oscillating follower | High accuracy |
Motion Profiles
Common profiles:
1. Parabolic (constant acceleration)
s = (1/2) * a * t^2 for first half
Good: Simple, smooth
Bad: Infinite jerk at transition
2. Simple harmonic
s = (h/2) * (1 - cos(pi*t/T))
Good: Zero velocity at ends
Bad: Finite acceleration at ends
3. Cycloidal
s = h * (t/T - sin(2*pi*t/T)/(2*pi))
Good: Zero acceleration at ends
Bad: Higher peak acceleration
4. Modified trapezoid
Combines constant acceleration with transitions
Good: Low peak acceleration
Bad: More complex
Pressure Angle
tan(alpha) = (dy/dtheta) / (rb + y)
Where:
alpha = pressure angle
dy/dtheta = slope of displacement curve
rb = base circle radius
y = follower displacement
Limit: alpha < 30 degrees (typically)
Gear Train Design
Gear Types
| Type | Application | Efficiency | |------|-------------|------------| | Spur | Parallel shafts | 98-99% | | Helical | Parallel shafts, quieter | 97-99% | | Bevel | Intersecting shafts | 97-98% | | Worm | High ratio, non-reversing | 50-90% | | Planetary | Compact, high ratio | 97-98% |
Gear Ratios
Simple gear train:
i = N2/N1 = omega1/omega2
Compound gear train:
i_total = product of individual ratios
Planetary gear train:
i = 1 + Nring/Nsun (sun fixed)
i = 1/(1 + Nsun/Nring) (ring fixed)
Gear Geometry
Module: m = d/N
Pitch: p = pi * m
Addendum: a = m
Dedendum: b = 1.25 * m
Center distance: C = m * (N1 + N2) / 2
Contact ratio:
CR = (Arc of action) / (Circular pitch)
Minimum CR > 1.2 recommended
Dynamic Analysis
Force Analysis
Newton-Euler method:
Sum F = m * a_g (for each link)
Sum M_g = I_g * alpha (about mass center)
D'Alembert approach:
Add inertia forces: -m*a, -I*alpha
Solve as static equilibrium
Shaking Forces and Moments
Shaking force = -Sum(m_i * a_i)
Shaking moment = -Sum(I_i * alpha_i + r_i x m_i * a_i)
Balancing strategies:
1. Add counterweights
2. Optimize mass distribution
3. Use multiple cylinders (phase)
Process Integration
- Cross-cutting for mechanical system design processes
Input Schema
{
"mechanism_type": "linkage|cam|gear|custom",
"motion_requirements": {
"input_motion": "rotation|translation",
"output_motion": "rotation|translation",
"motion_profile": "string or array",
"speed": "number (RPM or m/s)"
},
"constraints": {
"space_envelope": "object",
"force_requirements": "number",
"accuracy": "number"
},
"operating_conditions": {
"load": "number",
"speed_range": "array [min, max]",
"duty_cycle": "string"
}
}
Output Schema
{
"mechanism_design": {
"type": "string",
"configuration": "object",
"link_dimensions": "array"
},
"kinematic_results": {
"position_analysis": "array or function",
"velocity_analysis": "array or function",
"acceleration_analysis": "array or function",
"transmission_angle": "number"
},
"dynamic_results": {
"forces": "array",
"torques": "array",
"shaking_forces": "object"
},
"performance_metrics": {
"pressure_angle": "number (cams)",
"contact_ratio": "number (gears)",
"efficiency": "number"
},
"design_documentation": "reference"
}
Best Practices
- Start with kinematic requirements
- Check Grashof criterion for linkages
- Limit pressure angles in cams
- Verify adequate contact ratio for gears
- Analyze dynamics at operating speed
- Consider balancing for high-speed mechanisms
Integration Points
- Connects with CAD Modeling for geometry
- Feeds into FEA Structural for stress analysis
- Supports Test Planning for validation
- Integrates with Vibration Analysis for dynamics