© als geometric software s.a. – all rights reserved ggcm : the general geometric constraint...
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© ALS Geometric Software S.A. – All rights reserved
GGCM: The General Geometric Constraint Manager
Brief Technical Overview
GGCM in a nutshell
A next-generation, 2D/3D integrated, fully variational constraint manager.
◦ Input:• A set of geometric objects, curves, surfaces, assembly
parts, variables etc
• A set of complex constraints and equations
◦ Output: • A solution that satisfies all constraints and equations
• Analysis and diagnostic output.
© ALS Geometric Software S.A. – All rights reserved
Application areas
Technology-leading variational solving for:
• Assembly management
• Part design
• Robotics
• Curve and surface editing and optimisation
• Smooth kinematic motion simulation
• Constantly exploring many more (Operations research and optimisation, financial engineering, biochemistry, etc)
© ALS Geometric Software S.A. – All rights reserved
Non-linear equation solving
• GGCM is, in its heart, a non-linear equation solver.
• Based on breakthrough research and technology developed in-house.
• Superior in: Solvability Performance Behaviour
• Flexible and extensible.
• Equipped with a simple C/C++ API for integration into any Client software system.
• Accompanied by a configurable Client application.
© ALS Geometric Software S.A. – All rights reserved
© ALS Geometric Software S.A. – All rights reserved
A complete constraint manager
Natively supported GGCM objects:• Points, lines and planes
• Scalar variables
• Fully variational B-spline curves & surfaces
• Fully variational conic sections (ellipse, parabola, hyperbola)
Natively supported constraint types:• Distance, angle (sign & supplementarity allowed)
• Incidence for points, lines, planes
• Curve-point-incidence, Curve-line-tangency
• Symmetries
© ALS Geometric Software S.A. – All rights reserved
User-defined objects and constraints
• Power in the hands of the Application.
• Examples:
• Inequalities
Circles Cones
Tori Midpoint
Equality Symmetry
Areas and volume Gears
Screws Rack/pinion
Belts etc
© ALS Geometric Software S.A. – All rights reserved
Complex assembly interactions
© ALS Geometric Software S.A. – All rights reserved
Expression constraints
Extremely powerful Non-linear solving capabilities Engineering constraints Complex physical systems Curves and surfaces Etc.
© ALS Geometric Software S.A. – All rights reserved
Equilibrium analysis
Belt and pulley Hanging cable and spring
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• Needle always perpendicular to Bspline
Kinematics
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Curvature control
Convexity enforced
Convexity not enforced
Inequality constraints
Inequalities on joints
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Variational curves – cable definition
• Curve length constraint.
• Cable extends/retracts according to robot movement.
• Cable properties defined by expressions.
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Cables and collision avoidance
• Tighten cable avoiding collision
© ALS Geometric Software S.A. – All rights reserved
Soft fixing
• Soft fixing makes elements “heavier”
• Discrete and continuous modes
• Not absolute fixing: Things will move if they need to.
• E.g. two options:
• A) Make V heavier
• B) Make L heavier
• Movement of robot will try to respect relative “weight” of V and L.
© ALS Geometric Software S.A. – All rights reserved
Optimisation and soft fixing
• Rectangular body B travels along conveyor belt.
• Obstacle below the conveyor belt.
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Smooth surface manipulation
Elastic surface with embedded rigid bodies
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Modelling elasticity
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Different elasticity models
Modelling different elastic properties.
© ALS Geometric Software S.A. – All rights reserved
Diagnostics and analysis tools
• Failure diagnostics:
Identifies the smallest part of a failing problem. Error spotted at once. Far outclasses existing offerings.
© ALS Geometric Software S.A. – All rights reserved
• Stiffness (DoF) analysis:
Returns a list of objects / assembly parts that are stiff, i.e. have no degrees of freedom left.
• Rigid Equivalence Classes
Automatically identifies groups of objects that are forced to move rigidly, as a result of the constraints in the model.