© ALS Geometric Software S.A. – All rights reserved GGCM : The General Geometric Constraint...

© 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.

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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

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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

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Complex assembly interactions

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Expression constraints

Extremely powerful Non-linear solving capabilities Engineering constraints Complex physical systems Curves and surfaces Etc.

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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

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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.

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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.

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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.