Mechanism Synthesis Mechanisms synthesis In kinematic analysis a

Mechanism & Synthesis Mechanisms & synthesis In kinematic analysis, a given mechanism is investigated based on the mechanism geometry plus other known characteristics (such as input angular velocity, angular acceleration, etc. ). Kinematic synthesis, on the other hand, is the process of designing a mechanism to accomplish a desired task. Both choosing the types as well as the dimensions of the new mechanism can be part of kinematic synthesis

Mechanism & Synthesis 1. If one of the links of the kinematic chain is fixed , then it forms a mechanism. 2. Mechanism is used to transmit rotary or reciprocatory motion. • Mechanism with four links is known as simple mechanism and with more than four links is called compound mechanism. • When a mechanism is designed to produce power or do some work then it a machine.

Mechanism & Synthesis Degrees of freedom for plane mechanisms It is defined as number of input parameters that has to be individually controlled in order to bring the mechanism into useful engineering purpose. The definition of the degrees of freedom of a mechanism is the number of independent relative motions among the rigid bodies. Number of degrees of freedom is one.

Mechanism & Synthesis • • • F = total degrees of freedom in the mechanism n = number of links (including the frame) l = number of one degree of freedom pairs h = number of two degrees of freedom pairs This equation is also known as Gruebler's equation. The number of degrees of freedom of a mechanism is also called the mobility of the device. The mobility is the number of input parameters (usually pair variables) that must be independently controlled to bring the device into a particular position. The Kutzbach criterion, which is similar to Gruebler's equation, calculates the mobility.

Mechanism & Synthesis A four bar linkage comprises four bar-shaped links and four turning pairs Coupler Link output Link Input Link Fixed Link

Mechanism & Synthesis Terminology • • • In a four-bar linkage, we refer to the line segment between hinges on a given link as a bar where: s = length of shortest bar l = length of longest bar p, q = lengths of intermediate bar Grashoff's theorem states that a four-bar mechanism has at least one revolving link if s + l <= p + q

Mechanism & Synthesis Terminology • • • Crank: A side link which revolves relative to the frame is called a crank. Rocker: Any link which does not revolve is called a rocker. Crank-rocker mechanism: In a four bar linkage, if the shorter side link revolves and the other one rocks (i. e. , oscillates), it is called a crank-rocker mechanism. Double-crank mechanism: In a four bar linkage, if both of the side links revolve, it is called a doublecrank mechanism. Double-rocker mechanism: In a four bar linkage, if both of the side links rock, it is called a doublerocker mechanism.

Mechanism & Synthesis of four bar mechanism Let us consider a four bar mechanism for three different positions as shown in the figure.

Mechanism & Synthesis of four bar mechanism • • • Let the three positions of the input link AB are known and the three positions of the output link CD are also Known. To determine the dimensions of the links a, b, c and d given the three kinown angular positions of the input link and output link. The freudenstien equation: – K 1 cosθ + K 2 cosΦ+k 3= cos(θ – Φ) – Where K 1 = d/a, k 2=d/c, k 3= (a 2 -b 2 + c 2 + d 2 )/ 2 ac

Mechanism & Synthesis K 1= Δ 1/Δ , k 2= Δ 2/Δ , K 3= Δ 3/Δ. Assuming the value of either a or d other values are obtained. Here link dimensions are determined and the mechanism is graphically drawn on the canvas with the dimensions of the links.

Mechanism & Synthesis Interactivity • – – • Enter values of theta Input parameters Θ 1 , θ 2 and θ 3 Φ 1, Φ 2 and Φ 3. Enter values here Grey cells are input cells Output parameters – a, b, c, d the dimensions Do not touch of the links of four bar Output cells mechanism. Do not touch theta 1 theta 2 theta 3 delta Matrix delta Enter values of phi 30 45 60 0. 5 phi 1 phi 2 phi 3 60 45 30 0. 866 1 0. 7071067 0. 707 8 0. 8660254 0. 5 1 -0. 0176381 k 1 delta 1 0. 866025 Matrix 1 0. 707107 1 2. 7802 delta 2 Matrix Formual cells do not touch delta 1 -0. 0490381 k 2 2. 7802 k 3 -2. 932 1 1 0. 866025 0. 5 1 0. 5 0. 866025 1 0. 707107 1 1 0. 866025 1 delta 2 -0. 0490381 delta 3 0. 0517122 6 delta 3 Matrix 0. 5 0. 866025 0. 707107 0. 866025 a b c d = = 0. 36 1. 42 0. 36 1 0. 5 1 0. 866025

Mechanism & Synthesis Animation

Quality Engineering Management Quality Management In a four bar mechanism the lengths of input , floating and output links are respectively 300 mm, 400 mm and 150 mm. To have continuous motion with the designed mechanism the length of the fixed length should be o> 550 mm o<= 550 mm o 750 mm o 325 mm

Quality Engineering Management Quality Management In a double crank mechanism, the rotation of input link is 360 degrees then the rotation of output link is 180 degrees 360 degrees 450 degrees 90 degrees

Quality Engineering Management Quality Management The motion of input link, floating link and output link are of the following type respectively: o. Rotational, Rotational/ reciprocating, Rotational o. Linear , Linear o. Reciprocating, Rotational, Reciprocating o. Both reciprocating and rotary for all the three links.

Quality Engineering Management Quality Management Four bar mechanism is a o. Open loop kinematic linkage o. Closed loop kinematic linkage o. Open loop with 2 Degrees of freedom o. Is not a machine and mechanism

Mechanism & Synthesis Resources Books: Theory of machines by Thomas bevan Erdman & Sandor 84)Erdman, A. and Sandor, G. , Mechanism Design: Analysis and Synthesis, Prentice-Hall, New Jersey, 1984. Reference Links: http: //www. cs. cmu. edu/~rapidproto/mechanisms/ http: //www. softintegration. com/chhtml/toolkit/mechanism/fourbar_ani. html