Degrees of Freedom- Grubler and Kutzbach Equation скачать в хорошем качестве

Degrees of Freedom- Grubler and Kutzbach Equation

Structure, Mechanism, All the machines have working parts called –Mechanisms- If a number of bodies are assembled in such a way that the motion of one causes constrained and predictable motion to the other bodies , it is called a mechanism. Machines are a central part of life today. A machine is a mechanism or a combination of mechanisms which apart from imparting definite motions to the parts also transmits and modifies the available mechanical energy into some kind of desired work. A resistant body or a group of resistant bodies with rigid connections preventing their relative movement is known as link. A link is a member of a mechanism which when connected to other members have relative motion between them. A link is also known as an Kinematic link or Element. Classification- Links can be classified as Binary, ternary or quaternary depending upon their ends on which other links can be joined Binary Link, ternary link and Quaternary link Kinematic pair based on Nature of contact. 1.Higher pair ( Point or line Contact) 2.Lower pair (Surface or Area Contact) Kinematic pair based on Nature of Mechanical Constraint.1.Closed pair 2.Unclosed Pair Kinematic pair based on Nature of relative motion. 1.Sliding pair 2.Turning pair 3.Rolling pair 4.Screw pair 5.Spherical pair Lower pair (Area or Surface contact)- examples-Nut turning on screw,Universal joint,All parts of Slider crank mechanism Higher pair (Line or Point contact)- examples-Gears,Cam and Follower,Wheel Rolling on a surface Types of Joints 1.BINARY JOINT 2.TERNARY JOINT 3.QUATERNARY JOINT Degrees of Freedom An unconstrained body moving in space can possibly follow the following independent motions 1.Translational Motions along any three mutually perpendicular axes x, y and z. 2.Rotational Motions about these axes x, y and z. Thus a rigid body which is free to move in all the above possible motions has six(6) degrees of freedom. But the connection of link with other link imposes restraint on both the links . Degrees of Freedom= 6- Number of restraints imposed Mobility of Mechanisms 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. Gruebler's equation( Planar mechanisms)- The Kutzbach criterion, which is similar to Gruebler's equation, calculates the mobility