Unit_1_Lesson_3_-_Basics_of_Mechanisms.pptx.pdf
- 1. 1 io1071 Construeren/inleiding ME 33 - Theory of Machines Lesson 3 Grashof’s Law for a Planar Four-Bar Linkage
- 2. 2 io1071 Construeren/inleiding ME 33 - Theory of Machines • 4 link mechanism is the simplest of all closed loop mechanisms. • A four bar linkage comprises four bar-shaped links (.. Have 3 moving links; 1 fixed link; and 4 pin joints). • The four bar chain has four turning pairs (.. this is simplest type of kinematic chain/linkage in which four rigid links are connected by four pin joints). Input Link Coupler Link (opposite to the frame, transmits force from the input to output link) Output Link Fixed Link Grashof’s Law .. for a Planar Four-Bar Linkage … What is a Planar Four-Bar Linkage?
- 3. 3 io1071 Construeren/inleiding ME 33 - Theory of Machines • Crank: A link which can make complete revolution is known as crank. • Rocker: Any link which does not revolve is called a rocker. • Frame: The fixed link is known as frame. • Coupler/connecting rod: The opposite link of frame is known as connecting rod. Terminology ... • 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 double-crank mechanism. • Double-rocker mechanism: In a four bar linkage, if both of the side links rock, it is called a double-rocker mechanism. Grashof’s Law .. for a Planar Four-Bar Linkage …
- 4. 4 io1071 Construeren/inleiding ME 33 - Theory of Machines Grashof’s Law .. for a Planar Four-Bar Linkage … • Grashof’s Law states that for a planar four-bar linkage system, the sum of the shortest and longest link lengths cannot be greater than the sum of the remaining two link lengths if there is to be a continuous relative rotation between two members. • Mathematically, Suppose s= length of the shortest link l = length of the longest link p & q = lengths of other links s + l ≤ p + q -> if there is to be a continuous motion Note: if s + l > p + q, then no continuous relative motion is possible; i.e., if the above inequality is NOT satisfied, no link will make a complete revolution relative to another.
- 5. 5 io1071 Construeren/inleiding ME 33 - Theory of Machines • Consider a four-bar-linkage. Denote the smallest link by s , the longest link by l and the other two links by p and q . If s + l ≤ p + q, • then depending whether link s is connected to the ground by one end, two ends, or no end is connected, the mechanism can be one of the following types: Grashof’s Law and a Four-Bar-Linkage ... Grashof’s Law .. for a Planar Four-Bar Linkage …
- 6. 6 io1071 Construeren/inleiding ME 33 - Theory of Machines • Function: The main function of mechanism is to produce rotating, oscillating, and reciprocating motion from rotation of crank and vice versa. • Links can be used to convert: – Continuous rotation into another rotation motion – Continuous rotation into oscillation or reciprocation (or vice versa) – Continuous rotation into oscillation, or reciprocation into reciprocation • Kinematics of linkage mechanisms: – Function generator: relative motion between links connected to frame – Path generator: path of tracer point – Motion generator: motion of the coupler linkage Reciprocating motion is a repetitive up-and-down or back-and-forth linear motion. Found e.g. in reciprocating engines and pumps. Oscillating motion is swinging from side to side, like a pendulum in a clock.. Grashof’s Law .. for a Planar Four-Bar Linkage …
- 7. 7 io1071 Construeren/inleiding ME 33 - Theory of Machines • A variety of mechanisms can be found/created from a four link mechanism through slight variations such as: – Changing the character of a pair, e.g., from rotation to sliding, etc. – Proportion/size, e.g., length of the link. – Many complex mechanisms can be formed from combination of two or more such four link mechanisms Grashof’s Law .. for a Planar Four-Bar Linkage … Main types of Four- Link Mechanism Four bar Linkages (Double Crank Mechanism, Double Rocker Mechanism; Crank Rocker Mechanism) Slider Crank Mechanism
- 8. 8 io1071 Construeren/inleiding ME 33 - Theory of Machines • A crank-rocker mechanism Grashof’s Law and a Four-Bar-Linkage ... • A double crank (i.e., crank-crank) mechanism (… the shortest link is the frame - both input and output links can rotate through 360o). Grashof’s Law .. for a Planar Four-Bar Linkage … (… the shortest link can make a 360o revolution while the output link oscillates)
- 9. 9 io1071 Construeren/inleiding ME 33 - Theory of Machines • A rocker-rocker (double rocker) mechanism Grashof’s Law and a Four-Bar-Linkage ... Grashof’s Law .. for a Planar Four-Bar Linkage … (… the shortest link can make a 360o revolution but the pivoting links can only oscillate)
- 10. 10 io1071 Construeren/inleiding ME 33 - Theory of Machines • Grashof’s law is a very important consideration when designing a mechanism driven by a motor. • Grashof’s criteria is used to determine whether or not at least one of the links can rotate 360o. (… in mechanisms driven by motors, helps to ensure that the input crank can make a complete revolution.) Significance of Grashof’s Law…. Grashof’s mechanism (the Grashof condition is satisfied, s + l < p + q, and the shortest link can rotate 360o.) Non-Grashof’s mechanism (as the short link is moved around, the fact that s + l > p + q means that the short link cannot complete its revolution). Grashof’s Law .. for a Planar Four-Bar Linkage …
- 11. 11 io1071 Construeren/inleiding ME 33 - Theory of Machines Grashof’s Law .. for a Planar Four-Bar Linkage …
- 12. 12 io1071 Construeren/inleiding ME 33 - Theory of Machines End… Summary