Basics of Kinematic analysis in Mechanism design

Explore the mobility of planar mechanisms using the Kutzbach criteria to determine degrees of freedom and the number of independent inputs, by counting links and joints.

Use the mobility criteria to classify link configurations as mechanisms or structures by counting links, joints, and degrees of freedom from prismatic and other pairs.

Explore exceptions to Kutzbach mobility criteria using parallelogram linkages, showing how dimensions and link orientations can enable motion despite calculations predicting a structure, and emphasize practical verification.

Examine mobility criteria for planar and spatial mechanisms, derive single-degree-of-freedom forms using prismatic and revolute pairs, and analyze the universal joint and Stewart platform as practical examples.

Learn how selecting a single fixed link creates a frame of reference for a four-bar mechanism, producing multiple inversions such as slider mechanism variants and other motion cases.

Explore Grashof criterion for four-bar linkages, determining when the shortest and longest links allow full rotation, including crank and rocker, double crank, and parallelogram cases.

Analyze mechanism point positions using position vectors, distinguishing absolute and relative positions in fixed and moving frames, and apply vector addition and subtraction to describe straight and curvilinear motion.

Derive the loop closure equation for a four-bar linkage using vectors to determine the positions and orientations of A, B, C, and D in a fixed frame.

Explore the loop closure equation for a slider-crank mechanism, deriving vector relations from A to B, and solving for crank and slider positions using circle intersections and vector components.

Derive the absolute position of a point on the four-bar coupler using vector loop closure, vector diagram, and graphical construction from known link lengths.

Learn velocity analysis in mechanism design by defining linear, angular, and instantaneous velocity through omega cross r, and apply relative velocity with the velocity-difference vector via the vector triangle.

Explore velocity analysis of coupler in a four-bar mechanism using velocity vectors, omega one, omega three, and a velocity polygon to determine omega two and velocity of point C.

solve velocity analysis for a forward linkage by determining absolute velocities at points b, c, e, and f using velocity polygons and cad-based methods.

Develop velocity analysis for a four-bar mechanism, deriving angular velocities omega3 and omega4 and solving absolute velocities at points using relative velocity equations and velocity polygons.

Explore velocity analysis of a crank-slider mechanism, constructing velocity polygons to determine the instantaneous velocities and angular velocity of links using relative and absolute velocities.

Explore acceleration analysis in mechanism design by separating linear acceleration into tangential and normal components, driven by angular acceleration alpha and radius R, and apply relative acceleration concepts.

Perform acceleration analysis for the formal link by constructing velocity and acceleration polygons, determining angular accelerations of links three and four and the absolute acceleration at point b.

Explore acceleration analysis of a four-link locking mechanism using the acceleration polygon method, deriving velocity components, angular velocity, and the absolute accelerations of points B and C.

Develop acceleration analysis using an activation polygon to compute A, B, and C accelerations via components NCEA, NBA, NBC and ATC, yielding absolute, relative accelerations and angular acceleration.

Explore static and dynamic force analysis of mechanisms, using free body diagrams to assess external and internal forces, static equilibrium, inertia, and conditions for two- and three-force members.

Analyze static force analysis of a four-bar mechanism by drawing free-body diagrams, enforcing equilibrium for three-force members, and calculating the crank moment M1 two to hold link four.

conducts a static force analysis of a slider-crank mechanism, building free-body diagrams to determine the torque needed to maintain equilibrium; shows how frictionless assumptions change reaction forces.

Explore dynamic force analysis of planar mechanisms, linking unbalanced forces, inertia forces, and moments to angular acceleration via Dalembert's principle and the center of mass.

Solve the double slider mechanism problem by analyzing velocity and acceleration, compute the inertia force and inertia torque, and determine the angular acceleration and dynamic equilibrium.

Analyze a compact retractable wall-mounted seat using a planar double forbearer mechanism, covering problem statements, concept schemes, and 3D motion analysis in Fusion 360 with parametric link lengths.

Explore a window opening mechanism case study with a slider-rocker and prismatic link, applying kinematic analysis and parametric CAD motion to satisfy limited travel and a 15-degree opening.

Explore a case study of a high camber suspension system, modeled as a double rock'em mechanism, analyzing the wheel camber angle alpha during bump and rebound.

Explore a single windshield wiper mechanism powered by a four-bar linkage, analyzing design conditions, line diagrams, and how input crank rotation translates into wiper swing and angular velocity.

Explore case study 5, a press brake shear for cutting sheet metal, and develop a position diagram as the red shear angle reaches zero, determining other link angles.