Kinematics and Dynamics Vocab & Concepts

From lecture notes

Gaspard-Gustave de Coriolis (1792 -1843)

French Mechanical Engineer - Angular Acceleration & Coriolis effect

Paul Dirac (1902 - 1984)

English Physicist - Dirac Delta function → tool for modeling impulse in physics

Hero of Alexandria (~100BC)

Greek Mathematician - First known gears

Harry Ferguson (1884 - 1960)

Irish Engineer, Planetary gear paradox, Masson Ferguson

F.W. Lanchester (1868 - 1946)

English Engineer - Model T Ford transmission, automotive engineering

Vernon Gleasman (1912 - 2004)

American Engineer - Torsen differential, worm gear to improve torque distribution in vehicles

Charles-Augustin de Coulomb (1736 - 1806)

French Engineer - Dry friction (Coulomb friction)

Jean d’Alembert (1717 - 1783)

French Mathematician - Quasi-static equations, d’Alembert’s principle → simplifies dynamic analysis by incorporating inertial forces

Acceleration

Rate of change of velocity with respect to time (angular or linear)

Absolute acceleration

The total acceleration of a point relative to a fixed reference frame

Difference acceleration

The acceleration of one point in reference to another

Coriolis Acceleration

An additional acceleration that appears when an object moves within a rotating system

Axis of slip

The line axis along which relative motion occurs between two connected bodies

Jerk

The rate of change of acceleration with respect to time, to ensure smooth transitions in motion

Function Generation

Designing a cam t produce a specific follower motion

Cam motions

Types of motion a cam imparts to the follower

-Rise

-Dwell

-Fall

Rise

The follower moves upward or away from the camshaft center

Fall

The follower moves downward or returns toward the base position

Dwell

The follower remains stationary as the cam continues to rotate

Force-closed

Spring return

Form-closed

Mechanically constrained

Conjugate cam

A cam system using two profiles working together to drive the follower positively throughout the motion cycle

Desmodromic cam

A cam that uses two separate lobes or linkages to open and close the valve r follower (No springs)

Trapezoidal motion

Shaped like a trapezoid in the velocity graph

Pressure angle

Angle between the direction of follower motion and the normal to the cam surface - Affects efficiency and side loading

Axis of transmission/slip

Relative sliding or rolling between the cam and follower

Followers

Component moved by a cam, classified by shape or motion

Curved follower

Rounded contact surface

Flat follower

Flat face in contact with cam, simple but may produce higher contact stress

Rolling follower

Wheel or roller to roll along the cam surface

Sliding follower

Slides directly along the cam surface

Piecewise function

Cam displacement function made of multiple distinct equations over different intervals

Cycloidal dislacement

Smooth, periodic motion curve based on cycloid geometry - Zero jerk at ends, minimized vibration

Sinusoidal acceleration

Acceleration follows a sine wave - smooth cam design

Critical path motion

The minimum-time path required to move the follower through its sequence while satisfying constraints

Constant velocity motion

Follower has uniform velocity over a portion of cam rotation - Often trapezoidal

Intermittent motion

Starts and stops during cam rotation - Geneva Mechanism

Eccentricity

The offset distance between the camshaft center and the follower axis

Rolling cylinders

Simplified model for understanding gear interactin

Law of gearing

The common normal at the point of contact between a pair of teeth must always pass through the pitch point

Torque ratio

Ratio of output torque to input torque in a gear system, depends on gear radius and force application

Velocity ratio

Ratio of input speed to output speed, inversely proportional to gear sizes

Pitch diameter

Theoretical diameter where two meshing gears effectively contact and transmit motion

Pressure angle

The angle between the line of actin and the tangent to the pitch circle

Backlash

Clearance between mating gear teeth

Compound gears

Configuration of two or more gears mounted on the same shaftD

Differential

A gear assembly that allows two output shafts to rotate at different speeds

Kinematics

The study of motion without regard to forces

Kinetics

The study of forces and torques that cause motion

Three laws of motion

1. An object in motion stays in motion

2. F=ma

3. For every action there is an equal and opposite reaction

Dynamic model

Simplified representation of a system that preserves mass and inertia properties so its dynamic matches the original

Mass moment of Inertia

Measures an objects resistance to angular accelerating around an axis

Center of mass/gravity

The point at which the entire mass or weight of a body is balanced

Parallel axis theorem

A method to calculate the moment of inertia about any axis

I=I_cm+md²

Through variables (Power Transmission)

Flow-based (e.g., force, torque, current)

Across variables (Power Transmission)

Potential-based (e.g., velocity, voltage)

Power

=Through x Across

Centrifugal Force

The apparent outward force in a rotating frame (Fictitious force)

Centripetal Acceleration

Inward force that keeps an object in circular motion

Virtual work

A method to analyze mechanical systems using imaginary displacements, useful for determining equilibrium

Kinetostatic

Analyzing by starting with known motion and working backwards to find forces

Matrix approach to linkage dynamics

Uses matrices to model the dynamics of complex linkages

[A][B]=[C]

[A]→Geometric Information

[B]→Unknown forces and Torques

[C]→Dynamic information

SGN ()

Sign function that returns the sign of a number, used for friction

Shaking force and moment

Unbalanced forces and moments caused by moving parts in a mechanism, transmit vibrations to the frame

Flywheel

A rotating mass used to store rotational energy and smooth out speed fluctuations