Mechanism design

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

1. Start with kinematic requirements
2. Check Grashof criterion for linkages
3. Limit pressure angles in cams
4. Verify adequate contact ratio for gears
5. Analyze dynamics at operating speed
6. 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