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GEOMETRICCONSTRAINTSAlso known as “Sketch Relations” in SolidWorksLecture 5MAE 455 Computer-Aided Drafting and Design

2D Geometric ObjectsGeometric ObjectDeg.-offreedomEquationPointInfinite straight line2NA2𝑦 𝑚𝑥 𝑏Alternative form:𝑥 sin 𝛼 𝑦 cos 𝛼 𝑑 0Straight line segment4Parametric form:𝑥 𝑥1 𝑥2 𝑥1 𝑡𝑦 𝑦1 𝑦2 𝑦1 𝑡0 𝑡 1Variablesthat need to bespecifiedx, ym, bor𝛼, 𝑑x1, y1, x2, y2(Note that t is an extra parameter that can beeliminated by combining the two equations.)Circle3𝑥 𝑥𝑐 2 𝑦 𝑦𝑐 2 𝑟 2Alternative parametric form:𝑥 𝑥𝑐 𝑟 𝑐𝑜𝑠 𝑡𝑦 𝑦𝑐 𝑟 𝑠𝑖𝑛 𝑡0 𝑡 2𝜋xc, yc, r

2D Geometric ObjectsGeometric ObjectDeg.-offreedomCircular arc5Ellipse5Equationthat need to bespecified𝑥 𝑥𝑐 𝑟 𝑐𝑜𝑠 𝑡𝑦 𝑦𝑐 𝑟 𝑠𝑖𝑛 𝑡𝑡1 𝑡 𝑡2𝑥𝑠ℎ𝑎𝑝𝑒 𝑎 𝑐𝑜𝑠 𝑡𝑦𝑠ℎ𝑎𝑝𝑒 𝑏 𝑠𝑖𝑛 𝑡𝑥 𝑥𝑐 𝑥𝑠ℎ𝑎𝑝𝑒 𝑐𝑜𝑠 𝜃 𝑦𝑠ℎ𝑎𝑝𝑒 𝑠𝑖𝑛 𝜃𝑦 𝑦𝑐 𝑥𝑠ℎ𝑎𝑝𝑒 𝑠𝑖𝑛 𝜃 𝑦𝑠ℎ𝑎𝑝𝑒 𝑐𝑜𝑠 𝜃0 𝑡 2𝜋Parabola4Variables𝑥𝑠ℎ𝑎𝑝𝑒 𝑡𝑦𝑠ℎ𝑎𝑝𝑒 𝑎 𝑡 2𝑥 𝑥𝑐 𝑥𝑠ℎ𝑎𝑝𝑒 𝑐𝑜𝑠 𝜃 𝑦𝑠ℎ𝑎𝑝𝑒 𝑠𝑖𝑛 𝜃𝑦 𝑦𝑐 𝑥𝑠ℎ𝑎𝑝𝑒 𝑠𝑖𝑛 𝜃 𝑦𝑠ℎ𝑎𝑝𝑒 𝑐𝑜𝑠 𝜃xc, yc, r , t1, t2a, b, xc, yc, θNote that a and bare DOF related toshape and xc, yc, are DOF related torigid body motion.a, xc, yc, θNote that a is DOFrelated to shapeand xc, yc, areDOF related torigid body motion.

2D Geometric ObjectsGeometric ObjectFreeform (e.g., b-spline)(Shape is fixed as:𝑥𝑓𝑓 𝐹𝑥 (𝑡)𝑦𝑓𝑓 𝐹𝑦 (𝑡)0 𝑡 1but can be scaled, translated and rotated.)Deg.-offreedom4EquationVariablesthat need to bespecified𝑥𝑠ℎ𝑎𝑝𝑒 𝑠𝑥𝑓𝑓𝑦𝑠ℎ𝑎𝑝𝑒 𝑠𝑦𝑓𝑓𝑥 𝑥𝑐 𝑥𝑠ℎ𝑎𝑝𝑒 𝑐𝑜𝑠 𝜃 𝑦𝑠ℎ𝑎𝑝𝑒 𝑠𝑖𝑛 𝜃𝑦 𝑦𝑐 𝑥𝑠ℎ𝑎𝑝𝑒 𝑠𝑖𝑛 𝜃 𝑦𝑠ℎ𝑎𝑝𝑒 𝑐𝑜𝑠 𝜃s, xc, yc, θNote that xff andyff are fixed – notfree. s must bespecified forscaling and xc, yc, are DOF related torigid body motion.

2D Geometric Constraints Dimensional:––––Distance (linear, horizontal, vertical)AngleRadius (or diameter)Curve Length Geometric––––––Coincident, IncidentParallel, PerpendicularTangent, ConcentricMirrorSame Radius, Same LengthFixed, Fixed Horizontal, Fixed Vertical

2D Geometric dicularParallelDeg.-of-freedom 11NANANA

2D Geometric ConstraintsConstraintEquationDistance (P1, P2, s)(xP 2 xP1 )2 ( yP 2 yP1 )2 s 2Distance (L1, L2, s)d L 2 d L1 sDistance (P, L, s)xP cos L y P sin L d L sAngle (L1, L2, ) L 2 L1

2D Geometric ConstraintsConstraintEquationCoincident (P1, P2)xP 2 xP1 ;yP 2 yP1Coincident(L1, L2) L 2 L1 ;d L 2 d L1Incident(P, L)xP cos L yP sin L d L 0Fix (P) (at 10, 5)xP 2 10 ;yP 2 5

Under/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 d576647

How Under/Over-Constrained Geometry isIdentified in SolidWorksUnder-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 “(?)”.

Multiple Solutions These two shapes have the exact same geometric objects and constraints35235222661010 SolidWorks has a button on the Dimension Property Manager toflip between two solutions.

Constraining 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.12

Be careful!1. “Dangling” relations occur when constraining againstgeometry outside the sketch. If this geometrydisappears, the relation needs to be repaired.2. There is a difference between constraining the lengthof a line versus constraining the distance betweenlines. The constraint must reflect your design intent.versus

Potential Exam QuestionWhat constraints could be added to fully constrain thewireframe shown? Include constraints to remove rigid bodymotion.Vertices: A, B, C, DStraight Lines: AB, BC,CD, DARef2DCABRef314Ref1

Potential Exam QuestionSketch the figure resulting when the following constraints aresatisfied for the following objects.ObjectsVertices: A, B, C, DStraight Lines: AB, BC, CDCircular Arc: DAConstraintsCoincident (A, Ref1)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 A)Ref1

Also known as “Sketch Relations” in SolidWorks Lecture 5 MAE 455 Computer-Aided Drafting and Design. 2D Geometric Objects Geometric Object Deg.-of-freedom Equation Variables that need to be specified Point Infinite stra