1. © ALS Geometric Software S.A. – All rights reserved GGCM : The General Geometric Constraint Manager Brief Technical Overview

2. 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

3. 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

4. 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

6. 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

7. User-defined objects and constraints Power in the hands of the Application. Examples: Inequalities CirclesCones ToriMidpoint EqualitySymmetry Areas and volumeGears ScrewsRack/pinion Beltsetc © ALS Geometric Software S.A. – All rights reserved

9. Extremely powerful Non-linear solving capabilities Engineering constraints Complex physical systems Curves and surfaces Etc. © ALS Geometric Software S.A. – All rights reserved

10. Belt and pulleyHanging cable and spring © ALS Geometric Software S.A. – All rights reserved

11. Needle always perpendicular to Bspline © ALS Geometric Software S.A. – All rights reserved

12. Curvature control Convexity enforced Convexity not enforced Inequality constraints Inequalities on joints © ALS Geometric Software S.A. – All rights reserved

13. Curve length constraint. Cable extends/retracts according to robot movement. Cable properties defined by expressions. © ALS Geometric Software S.A. – All rights reserved

14. Tighten cable avoiding collision © ALS Geometric Software S.A. – All rights reserved

15. 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

16. Rectangular body B travels along conveyor belt. Obstacle below the conveyor belt. © ALS Geometric Software S.A. – All rights reserved

17. Elastic surface with embedded rigid bodies © ALS Geometric Software S.A. – All rights reserved

19. Modelling different elastic properties. © ALS Geometric Software S.A. – All rights reserved

20. 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.