Mechanisms Instructor: Shuvra Das Mechanical Engineering Dept. University of Detroit Mercy

Flowchart of Mechatronic Systems 3

Mechanism A mechanism is a device which transforms motion in a desirable pattern. e.g. linear motion to rotational motion, motion in one direction to motion in another direction A machine consists of mechanisms that are designed to produce and transmit motion in a certain pre-defined manner. Examples: Slider crank mechanism, transforms rotation into translation quick-return mechanism, less time spent per cycle in idling

Mechanism Example

Web Based Simulations Quick return mechanism: http://www.technologystudent.com/cams/crank1 htm. http://www.ul.ie/~kirwanp/linkstoanimations.htm http://www.innerauto.com/innerauto/htm/anim.html http://www.walterruffler.de/Animat.html

Elements in a mechanism Some of the elements:linkages, cams, gears, rack-and-pinion, chains, belt drives, etc. Linkages-----can be designed to perform a variety of different tasks. Cams ----- cam profile can be designed to prescribe motion in a particular manner. gears, chains, belts --- transform rotary motion from one axis to another. rack-and -pinion ---- transforms rotational motion to linear motion.

Kinematics Dynamics: Kinematics and Kinetics Kinematics: motion analysis without taking into consideration the forces that are involved Kinetics: study of the forces and energy associated with motion in mechanisms Mechanisms are made of links and joints

Links Links: rigid bodies capable of transmitting force with negligible deformation Binary Ternary Quarternary

Joints Joints: Revolute, sliding, helical, rolling, cylindric, planar, global universal (ball and socket)

Kinematic Chains A sequence of joints and links is called the kinematic chain. For a chain to transmit motion one link must be fixed and movement of one link will then produce predictable relative movement. It is possible to use the same mechanism to generate different types of motion depending on how the system is driven.

Mechanism Example

Four bar mechanism

Mechanisms Types of basic motions: pure rotation (roller with no sliding) pure translation (pure sliding with no rolling) Combined motions: sliding and rolling links moving together.

Degrees of Freedom Number of independent co-ordinates needed to determine the position of a link with respect to the ground.

Degrees of Freedom A rigid body can have a very complex motion which is a combination of translation and rotation motion, e.g. your hand moving towards an object. A 3-D object that is not constrained in any way is free to translate in 3 mutually perpendicular directions (x, y and z) and is free to rotate about three mutually perpendicular axes (x, y, and z). Hence, a 3-D rigid body that is unconstrained has 3 degrees of translation freedom and 3 degrees of rotational freedom (i.e. a total of six degrees of freedom).

Degrees of Freedom Consider a binary link: If it is lying freely in a 2-D plane it has 3 degrees of freedom: X and Y co-ordinate of any point on the link and its orientation with respect to a fixed axis (e.g. q with respect to the x axis) If a revolute or pinned joint is used to tie down a point it loses 2 degrees of freedom and one rotational degree of freedom remains.

Degrees of Freedom Number of degrees of freedom: 3(n-1)-2j; n = total number of links, (n-1) = number of movable links, j = number of joints.

Degrees of freedom N=10, j=12 dof=3(10-1)-2(12)=3

Degrees of freedom N=6, j=7 dof=3(6-1)-2(7)=1

Position Analysis of 4-bar Mechanism

Position Analysis of 4-bar Mechanism Points A and D are fixed to the ground and link 4 is the ground link. Links AB, BC and CD are movable. The position analysis is a mathematical representation of the vector sum of the 4 links in the system and is also known as the loop equation. Its representation is as follows: R1 e(iq1) + R2 e(iq2) = R3 e(iq3) + R4 e(iq4) R1(Cos q1+i Sin q1)+R2(Cosq2 +iSin q2) = R3(Cosq3 +iSinq3) + R4 (Cosq4 + iSinq4) R1 Cos q1+ R2 Cos q2 = R3 Cos q3 + R4 Cos q4 (R1 Sin q1+ R2 Sin q2)i = (R3 Sin q3 + R4 Sin q4)i

Position Analysis of 4-bar Mechanism R1 Cos q1+ R2 Cos q2 = R3 Cos q3 + R4 Cos q4 R1 Sin q1+ R2 Sin q2 = R3 Sin q3 + R4 Sin q4

Gear Trains Gear types: spur bevel helical worm

Velocity ratio of Gears wA/wB = -(NB / NA) = -(dB / dA) NB = number of teeth in B NA= number of teeth in A dA= pitch diameter of A dB= pitch diameter of B Gear trains: A series of intermeshed gear wheels

Velocity ratio of Gears Types of gear trains used: simple, compound, planetary. For simple gear trains: wA/wD = (wA/wB )(wB/wC)(wC/wD ) = (-NB/NA)(-NC/NB)(-ND/NC)= -(number of teeth in D / number of teeth on A) = -(Pitch diameter of gear D / Pitch diameter of gear A); B and C are idler gears: they help in changing direction of rotation only!!!

Velocity Ratio of Gears For a compound gear train:wA/wD = (wA/wB )(wB/wC)(wC/wD ) = (wA/wB )(wC/wD ) (if B and C are on the same shaft) = +(NB)(ND) / (NA)(NC) IF A has 30 teeth, B has 45, C has 36 and D has 18 45x18/(30X36)=3/4 if input is at 150 rpm output is 150/3/4=200