MAE 455 Computer-Aided Design and DraftingGeometric ConstraintsAlso known as“Sketch Relations” in SolidWorksMAE 455 Computer-Aided Design and Drafting22D Geometric ObjectsGeometric Object Deg.-of-freedom Point Infinite straight line Straight line segment Circle Circular arc Ellipse Parabola Freeform (e.g. b-spline)MAE 455 Computer-Aided Design and Drafting32D Geometric ObjectsObject Equation Point Infinite line Line seg. CircleMAE 455 Computer-Aided Design and Drafting42D Geometric ObjectsObject Equation Circular arc Ellipse Parabola FreeformMAE 455 Computer-Aided Design and Drafting52D Wireframe Constraints• Dimensional:– Distance (linear, horizontal, vertical)– Angle– Radius (or diameter)– Curve Length• Geometric– Coincident, Incident– Parallel, Perpendicular– Tangent, Concentric– Mirror– Same Radius, Same Length– Fixed, Fixed Horizontal, Fixed VerticalMAE 455 Computer-Aided Design and Drafting62D Wireframe ConstraintsConstraint Deg.-of-freedom removed Point-Point Line-Line Point-Line Distance Incident Angle Perpendicular Parallel 1 2 N/A N/A N/A 2 2 1 1 1 1 1 N/A N/A N/AMAE 455 Computer-Aided Design and Drafting72D Wireframe ConstraintsConstraint Equation Distance (P1, P2, s) Distance (L1, L2, s) Distance (P, L, s) Angle (L1, L2, θ) ()()2212212syyxxPPPP=−+− sddLL=−12 sdyxLLPLP=−+ααsincos θαα=−12 LLMAE 455 Computer-Aided Design and Drafting82D Wireframe ConstraintsConstraint Equation Coincident (P1, P2) Coincident(L1, L2) Incident(P, L) Fix (P) (at 10, 5) 12 PPxx=; 12 PPyy= 12 LLαα=; 12 LLdd= 0sincos=−+LLPLPdyxαα 102=Px; 52=PyMAE 455 Computer-Aided Design and Drafting9Under/Over-Constrained Geometry• If there are not enough constraints, then the geometry is under-constrained.• If there are too many constraints, then the geometry is over-constrained.7575466Under-constrained Over-constrainedMAE 455 Computer-Aided Design and Drafting10How Under/Over-Constrained Geometry is Identified in SWUnder-constrained:• Curves are blue.• Curves and points can be dragged.Over-constrained curves are yellow.Well-constrained curves are black (or red if there is no solution).Feature Manager also shows whether a sketch is:• under-constrained “(-)”• over-constrained “!”• unsolvable “(?)”.MAE 455 Computer-Aided Design and Drafting11Multiple Solutions• These two shapes have the exact same geometric objects and constraints3 5 210623 5 21062• Make a dimension negative to flip between two solutions.MAE 455 Computer-Aided Design and Drafting12Constraining Procedure1. Create Sketch (operation in construction history)2. Sketch curves3. Restrain rigid body motion. (Constrain against something that is not in sketch.)4. Constrain the points and curves of the sketch with respect to each other.MAE 455 Computer-Aided Design and Drafting131. “Dangling” relations occur when constraining against geometry outside the sketch. If this geometry disappears, the relation needs to be repaired.2. There is a difference between constraining the length of a line versus constraining the distance between lines. The constraint must reflect your design intent.Be careful!versusMAE 455 Computer-Aided Design and Drafting14Potential Exam QuestionWhat constraints could be added to fully constrain the wireframe shown? Include constraints to remove rigid body motion.Vertices: A, B, C, DStraight Lines: AB, BC, CD, DABACDRef2Ref1Ref3MAE 455 Computer-Aided Design and Drafting15Potential Exam QuestionSketch the figure resulting when the following constraints are satisfied for the following objects. A has been drawn to start you off.ObjectsVertices: A, B, C, DStraight Lines: AB, BC, CDCircular Arc: DAConstraintsFixed (A)Horizontal (AB)Distance (A, B, 2 in.) (B to the right of A)Angle (AB, BC, 45°) (up and to the right)Distance (AB, CD, 1 unit) (CD above AB)Tangent (DA, AB)Tangent (DA, CD) (DA left of