Kinematics of Machines: From Basics to Motion Analysis

Identify kinematic links as moving machine components and explore rigid, flexible, and fluid links, with piston and crank and hydraulic examples converting input motion into output.

Identify completely, incompletely, and successfully constrained motions with examples: square rod in a square hole; circular shaft in a circular hole with collars; and a shaft in a footstep bearing.

Explore kinematic pairs, where two links constrain relative motion to achieve machine output. Classify by motion (sliding, turning, rolling, screw, spherical), contact (lower, higher), and closure (self-closed, force-closed), with examples.

Understand kinematic chains formed by linking kinematic pairs from a fixed first link to the last, using crank and rocker and four-bar examples, plus L and J relations.

Explore binary, ternary, and quaternary joints in a chain and how to count them to assess kinematic feasibility using the relation j = 3/2(l-2) (no higher pairs), with practical examples.

Analyze degrees of freedom in plane mechanisms using the Kutzbach criteria. Apply n = 3(l-1) - 2j - h to assess movability across link–joint configurations.

Inversion of mechanism fixes different links in a four-bar kinematic chain to produce four distinct mechanisms, inversions, with outputs relative to the input.

Explore four-bar chains, including crank, driver, coupler, and lever configurations, governed by Grashof's law, and examine how inversions convert rotary motion to oscillatory, straight-line, or reciprocating motion.

Examine the single slider crank chain, a four-link mechanism with turning pairs and a sliding pair that converts crank rotation to piston motion, detailing five inversions including pendulum pump.

Investigate the double slider crank chain, with two turning pairs and two sliding pairs, and its three inversions: elliptical tremors, scotch yoke, and Oldham's coupling.

Learn to compute the velocity of a point on a link using instantaneous center method, comparing it with the relative velocity method and applying velocity relationships on a rigid link.

Explore how to determine the number and types of instantaneous centers in a four-bar mechanism, using the formula n(n-1)/2, and distinguish fixed, permanent, and neither fixed nor permanent centers.

Explore how the instantaneous center varies with link configurations, from pin joints and rolling contacts to slider motion, including centers at contact, center of curvature, and infinity.

Explain Arenhold Kennedy theorem: three instantaneous centers of moving bodies lie on a straight line, with centers ipk and ipr, and third center on the same line for four-bar linkages.

Explain relative velocity of bodies p and q moving in parallel lines with vp > vq, using vp q = vp − vq and vq p = vq − vp.

Apply the relative velocity method to a rigid link, showing that the velocity between any two points is perpendicular to the link and relates to omega and the segment lengths.

Learn to compute velocities of points p and q on a rigid link using the relative velocity method, construct velocity diagrams, and derive omega from v_p and pq.

Calculate the velocities in a slider crank mechanism using the relative velocity method to obtain the absolute and relative velocities of the crank, connecting rod, and slider.

Compute rubbing velocity at a pin joint as algebraic sum of angular velocities times the pin radius, using omega1 minus omega2 for same direction and plus for opposite.

Analyze the acceleration of a rigid link by decomposing it into radial (centripetal) and tangential components using omega and alpha for point q relative to p on link pq.

Construct the acceleration diagram for a rigid link to compute a point’s acceleration by combining radial and tangential components from a reference point, yielding total acceleration and angular acceleration.

Explains how to analyze acceleration in the slider crank mechanism, detailing radial and tangential components, velocity relations, and construction of the acceleration diagram for the slider and connecting rod.

Apply the instantaneous center method to a four-bar mechanism, locate all centers with a circle diagram and Kennedy theorem, and determine the velocity of QR from PQ’s angular velocity.

Apply the relative velocity method to a four-bar chain, using a space and velocity diagram to compute the angular velocity of link rs when s is at 50 degrees.

Explore the relative velocity method for a steam engine crank-slider mechanism, calculating piston velocity, connecting-rod angular velocity, point velocities, and rubbing velocities using velocity and space diagrams.

Apply velocity and acceleration diagrams to solve a slider-crank mechanism problem, determining the midpoint velocity and the connecting rod's angular velocity and acceleration at a crank angle of 60 degrees.