How to Make a Scissor Lift with Popsicle Sticks and Dowels

Parallelograms have opposite sides parallel and equal, opposite angles equal, and consecutive angles summing to 180°. Rhombuses have all sides equal, diagonals bisecting at 90°, and area = (d1 × d2)/2. Isosceles triangles have two equal sides and two equal base angles. The altitude from the vertex bisects the base and the vertex angle.

Six key properties of parallelograms and rhombuses: (1) In a parallelogram, opposite sides are equal; (2) A rhombus has four equal sides; (3) A rhombus is a special type of parallelogram with two adjacent sides equal; (4) The diagonals of a parallelogram bisect each other at their midpoints; (5) Cutting a parallelogram along its diagonal produces two congruent triangles; (6) The diagonals of a rhombus are perpendicular to each other.

This segment explores rhombus properties and triangle congruence. The diagonals of a rhombus are perpendicular, intersecting at 90 degrees. The reflexive property establishes that any segment is congruent to itself. The Side-Side-Side (SSS) postulate states that if three sides of one triangle equal three sides of another, the triangles are congruent. Linear pairs are adjacent angles formed by intersecting lines that are supplementary (sum to 180 degrees). Congruent supplementary angles are right angles. Each diagonal of a rhombus bisects opposite angles, dividing them into equal parts. In a rhombus, the diagonals create congruent triangles. Opposite sides of a parallelogram are congruent. Corresponding parts of congruent triangles are congruent (CPCTC).

A parallelogram has opposite sides parallel and equal, opposite angles equal, adjacent angles supplementary (180°), and diagonals that bisect each other. The diagonals divide the parallelogram into two congruent triangles and four equal-area triangles. A rhombus is a parallelogram with all four sides equal, diagonals perpendicular to each other, and diagonals that bisect the vertex angles.

A rhombus is a quadrilateral with four congruent sides. It is a special type of parallelogram because it has two pairs of opposite congruent sides. Since all four sides are congruent, opposite sides are automatically congruent to each other, satisfying the sufficient condition for a parallelogram. Therefore, all properties of parallelograms apply to rhombuses, including opposite angles being congruent, adjacent angles being supplementary, and diagonals bisecting each other.

This section introduces three fundamental types of forces and their corresponding stresses in materials. Tensile forces cause stretching and produce tensile stress (σ = F/A), calculated using the cross-section area. Compressive forces cause shortening and produce compressive stress, using the same formula. Shear forces cause sliding at contact surfaces and produce shear stress, but use the shear area instead of cross-section area. Direct stresses encompass both tensile and compressive stresses. A critical principle is that maximum direct stress always occurs at the smallest cross-section area, which is essential for engineering design to identify potential failure points.

Normal stress manifests as tension (pulling apart, stresses point outward) or compression (pushing together, stresses point inward), depending on load direction. Shear stress (τ) acts parallel to the section plane and follows specific nomenclature: the first subscript indicates the plane (e.g., τzy acts on z-plane), the second indicates direction (e.g., τzy acts in y-direction). Average shear stress is τ_avg = V/A, where V is internal shear force. These concepts are essential for analyzing different loading conditions in structural members.

This section establishes foundational concepts in structural mechanics. Tension is an upward force experienced when hanging a weight from a material like piano wire, while compression is a downward force acting along supports such as table legs. Stress is defined as force divided by cross-sectional area, enabling calculation of tensile and compressive stresses. Shear force emerges when forces do not act collinearly—for instance, when a beam rests on two supports with weight at its center, creating a tendency to shear along a plane perpendicular to the beam's axis. In ship structures, rivets experience shear forces as plates attempt to move in opposite directions. These principles form the basis for understanding structural behavior in engineering applications.

This section covers the three fundamental types of stress in materials. Tensile load (तनाव भार) is a pulling force (पुलिंग फोर्स) that pulls materials apart, causing tensile stress. Compressive load (संपीडन भार) is a pushing force (पुशिंग फोर्स) that pushes materials together, causing compressive stress. The fundamental stress formula σ = F/A applies to all stress types, with specific formulas for tensile (σt = Ft/A) and compressive (σc = Fc/A) stress. Shear stress (शियर स्ट्रेस) is also called transverse stress (ट्रांसवर्स स्ट्रेस) or अपरूपण प्रतिबल, developing when forces act parallel to surfaces rather than perpendicular. A riveted joint (रिवेट जॉइंट) is used as a practical example where shear stress develops when forces are applied parallel to the joint. The instructor provides visual demonstrations showing how tensile forces cause elongation, compressive forces cause shortening, and shear forces cause sliding and shape change.

This section covers the three fundamental forces acting on materials: tension (pulling apart), compression (pushing inward/crushing), and shear (ripping apart in opposite directions). It then introduces stress as the internal force per unit area that develops within materials when external forces are applied. For axial forces, stress (σ) equals force divided by cross-sectional area perpendicular to the force. For shear forces, shear stress (τ) equals force divided by the area parallel to the force direction. The unit for stress is Newton per meter squared (N/m²), also called the Pascal.

The pivot point is where the blade rotates to open and close the knife. Friction at the pivot point can cause sticky or sluggish action. This friction can be caused by misalignment, debris, or improper washer installation. Quality knives should have smooth, friction-free pivot action.

When a body is about to slide at one support but pivots at another, the pivot point experiences no friction force (or friction below maximum). To analyze this case, take moments about the pivot point to eliminate the unknown friction force at that point. This simplifies the calculation and allows you to solve for the applied force required to initiate motion.

A pivot joint (liaison pivot) is a mechanical connection that enables rotational movement between two components while maintaining their relative orientation. Three technological solutions exist: shoulder joints with retaining rings, key and keyway systems, and threaded fasteners. Pivot joints are classified into three categories: direct contact between shaft and housing, bushing (coussinet) implementations, and rolling bearing systems. Direct contact pivot joints offer simple mounting but suffer from low power transmission capability, surface wear, and friction-related power losses. Bushings reduce friction by providing a bronze intermediary layer between contacting surfaces.

Friction between moving parts in articulated systems can cause binding and prevent smooth operation. To reduce friction, bearings (roulements) should be placed at pivot points where parts connect. The placement of bearings is critical - they should be positioned to allow free movement without creating new contact points that cause friction. When building articulated systems, always consider where friction will occur and plan bearing placement accordingly.

Dans une liaison pivot imparfaite, les frottements se manifestent par des forces opposées qui s'exercent en différents points. Ces forces s'annulent globalement (résultante nulle) mais forment un couple résistant qui s'oppose à la rotation. Les frottements peuvent être modélisés de différentes façons : frottements solides (forces constantes) donnent un couple résistant constant, tandis que frottements fluides (proportionnels à la vitesse) donnent un couple résistant proportionnel à la vitesse angulaire. Pour une porte, les frottements solides donnent un couple constant, tandis que l'huile peut fluidifier les frottements.