Kinematic chain mechanism inversion_grashoff

kinematics

1. (Under the guidance of Prof. Rangaraj M Desai) Prepared by: Syed Zabuilla Chunkyraj Kh RU1441MDD007 RU1441MDD008 A Presentation on KINEMATIC CHAIN, MECHANISM, INVERSION & GRASHOFF’s LAW

2. Contents 2 Kinematic Chain Mechanism Inversion Grashoff’s Law

3. 3 KINEMATIC CHAIN : K inematic chain may be defined as a combination of kinematic pairs , joined in such a way that each link forms a part of two pairs and the relative motion between the links or elements is completely or successfully constrained. For example, the crankshaft of an engine forms a kinematic pair with the bearings which are fixed in a pair, the connecting rod with the crank forms a second kinematic pair, the piston with the connecting rod forms a third pair and the piston with the cylinder forms a fourth pair . The total combination of these links is a kinematic chain.

4. 4 Kinematic chain may be Open or Closed. In a closed kinematic chain, the distal segment is fixed and the end segments are unite to form a ring or a circuit. When one link moves all the other links will move in a predictable pattern. In an open kinematic chain, the distal segment terminates free in space. Each segment of an open chain has a characteristic degree of freedom of motion; the distal possessing a higher degree of freedom than the proximal ones. Link 1 Joint 1 Link 2 Joint 2 Joint 3 Link 3 Link 4 Open Kinematic Chain Link 1 Link 2 Link 3 Link 4 Link 5 Link 6 J1 J2 J3 J4 J6 J7 Closed Kinematic Chain

5. 5 Types of Kinematic Chains Four bar chain or quadric cyclic chain, Single slider crank chain, and Double slider crank chain. Fig 1 . Four bar chain or quadric cyclic chain ,

6. 6 Fig 2. Single slider crank chain, Fig 3. Double slider crank chain .

7. 7 MECHANISM : When one of the links of a kinematic chain is fixed, the chain is known as mechanism . It may be used for transmitting or transforming motion E.g. Slider-crank mechanism etc. Robotic arm ( Open type mechanism) Slider-Crank mechanism ( Closed type mechanism)

8. 8 INVERSION : Method of obtaining different mechanism by fixing different links in a kinematic chain, is Inversion . Inversions will have same relative motion between the links but absolute motion will change. No. of inversion = No. of links in kinematic chain. Example of Slider-crank Inversion: 1 2 3 4 Inversion #1 : Slider block translates 1 2 3 4 Inversion #2 : Slider block has complex motion

9. 9 GRASHOFF’s LAW : It states that for a Planar 4-bar linkage, Sum of the Shortest and the longest link lengths must be less than or equal to Sum of the remaining link lengths, if there is to be a continuous relative motion between 2 members. i.e. 1 2 3 4 Inversion #4 : Link 3 reciprocates 1 2 3 4 Inversion #3 : Slider block translates s l p q

10. 10 There are 3 inversions of 4-bar mechanisms, which are obtained by fixing different links of the kinematic chain. They are: Double Crank Mechanism Crank Rocker Mechanism Double Rocker Mechanism Double Crank mechanism: - When the shortest link is fixed, it gives double crank mechanism. A double crank converts rotary motion from a crank to a second crank or link in a different plane or axis. It is also known as crank-crank, drag-crank or rotary-rotary converter. The links p and l shown rotate through one complete revolution. This is one of the first inversions of four-bar mechanisms. Application: Coupling rod of locomotive (train wheels) etc. p l s q

11. 11 Crank-Rocker mechanism: - When any of the link adjacent to the shortest link is fixed, it gives crank rocker mechanism. A crank-rocker converts rotary motion from a crank to a reciprocating link in a different plane or axis or vice cersa . It is also known as crank-lever mechanism or a crank-rocker mechanism or a rotary-oscillating converter . The links s rotates and q reciprocates. - Application: Reciprocating engines/IC engines, Compressors etc. Double Rocker mechanism: - When the link opposite to the shortest link is fixed, it gives double rocker mechanism. A double rocker converts reciprocating motion from one link to another link in a different plane or axis. The links p and l reciprocates. Application:Windshield wipers, Quick return mechansism etc.

12. 12 References : Theory of Machines by R.S. Khurmi Kinematic of Machines Kinematic Fundamentals Mechanism by Ken Youssefi www.wikipedia.com

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