Theory of Machines - Revision history

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 == References ==
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Indicwiki: 23 revisions imported from :alpha:Theory_of_Machines

2022-12-16T04:11:09Z

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alpha>Ramamurthy S: Category added

2022-12-15T17:48:57Z

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alpha>Ramamurthy S: Content Modified

2022-12-14T06:05:32Z

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	<math>j = \frac{3}{2} L -2</math> .................... (1.2)		<math>j = \frac{3}{2} L -2</math> .................... (1.2)

	The equations (1.1) and (1.2) are applied only to kinematic chains having lower pairs. If they are applied to kinematic chains having		The equations (1.1) and (1.2) are applied only to kinematic chains having lower pairs. If they are applied to kinematic chains having higher pairs, then each higher pair must be taken equivalent to two lower pairs and an additional link.

	~~L.H.S = R.H.S then chain is constrainedhigher pairs, then each higher pair must be taken equivalent to two lower pairs and an additional link.~~ In equations (1.1) and (1.2) if		In equations (1.1) and (1.2) if

	L.H.S > R.H.S then chain is locked		* L.H.S > R.H.S then chain is locked
			* L.H.S = R.H.S then chain is constrained
	L.H.S < R.H.S then chain is unconstrained		* L.H.S < R.H.S then chain is unconstrained

	== External Links ==		== External Links ==

alpha>Ramamurthy S: Internal link added

2022-11-15T01:03:33Z

Internal link added

← Older revision		Revision as of 06:33, 15 November 2022
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	== Definition ==		== Definition ==
	Theory of Machines is a branch of science dealing with the study of relative [[motion]] between the various parts of a machine and forces which act on them.<ref>{{Cite book\|last=Bansal\|first=Dr. R. K.\|title=Theory of Machines\|pages=1}}</ref> Theory of Machines has two sub branches namely Kinematics and Dynamics.		Theory of Machines is a branch of science dealing with the study of relative [[motion]] between the various parts of a machine and forces which act on them.<ref>{{Cite book\|last=Bansal\|first=Dr. R. K.\|title=Theory of Machines\|pages=1}}</ref> Theory of Machines has two sub branches namely [[Kinematics]] and [[Dynamics]].

	Kinematics deals with the study of relative motion between the various parts of a machine. The force which act on them would be static in nature.		Kinematics deals with the study of relative motion between the various parts of a machine. The force which act on them would be static in nature.

	Dynamics deals with the study of relative motion between the various parts of a machine. The force which act on them would be static or dynamic in nature. Dynamics has two sub branches namely Kinetics and Statics.		Dynamics deals with the study of relative motion between the various parts of a machine. The force which act on them would be static or dynamic in nature. Dynamics has two sub branches namely [[Kinetics]] and [[Statics]].

	Kinetics is a branch of theory of machine which deals with various forces when the body is moving whereas Statics is a branch of theory of machine which deals with various forces when the body is stationary.		Kinetics is a branch of theory of machine which deals with various forces when the body is moving whereas Statics is a branch of theory of machine which deals with various forces when the body is stationary.

alpha>Ramamurthy S: Internal link added

2022-10-10T06:50:11Z

Internal link added

← Older revision		Revision as of 12:20, 10 October 2022
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	== Definition ==		== Definition ==
	Theory of Machines is a branch of science dealing with the study of relative motion between the various parts of a machine and forces which act on them.<ref>{{Cite book\|last=Bansal\|first=Dr. R. K.\|title=Theory of Machines\|pages=1}}</ref> Theory of Machines has two sub branches namely Kinematics and Dynamics.		Theory of Machines is a branch of science dealing with the study of relative [[motion]] between the various parts of a machine and forces which act on them.<ref>{{Cite book\|last=Bansal\|first=Dr. R. K.\|title=Theory of Machines\|pages=1}}</ref> Theory of Machines has two sub branches namely Kinematics and Dynamics.

	Kinematics deals with the study of relative motion between the various parts of a machine. The force which act on them would be static in nature.		Kinematics deals with the study of relative motion between the various parts of a machine. The force which act on them would be static in nature.

alpha>Ramamurthy S: Images updated

2022-09-23T08:34:40Z

Images updated

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	~~[[File:Degrees of freedom.png\|alt=Degrees of freedom\|thumb\|Fig 6. Degrees of freedom]]~~

	== Definition ==		== Definition ==
	Theory of Machines is a branch of science dealing with the study of relative motion between the various parts of a machine and forces which act on them.<ref>{{Cite book\|last=Bansal\|first=Dr. R. K.\|title=Theory of Machines\|pages=1}}</ref> Theory of Machines has two sub branches namely Kinematics and Dynamics.		Theory of Machines is a branch of science dealing with the study of relative motion between the various parts of a machine and forces which act on them.<ref>{{Cite book\|last=Bansal\|first=Dr. R. K.\|title=Theory of Machines\|pages=1}}</ref> Theory of Machines has two sub branches namely Kinematics and Dynamics.
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	#*Higher Pair - Two links has a point or line of contact between them. Example: Wheel rolling on a surface and Cam & follower		#*Higher Pair - Two links has a point or line of contact between them. Example: Wheel rolling on a surface and Cam & follower
	#According to the type of relative motion between the two links		#According to the type of relative motion between the two links
	#*~~[[File:Sliding Pair.jpg\|alt=Fig 2. Sliding Pair\|thumb\|Fig 2. Sliding Pair]]~~Sliding pair - Kinematic pair where the two links have a sliding motion relative to each other. Example : rectangle rod in a rectangular hole as shown in the fig 2 .		#*Sliding pair - Kinematic pair where the two links have a sliding motion relative to each other. Example : rectangle rod in a rectangular hole as shown in the fig 2 .[[File:Sliding Pair.jpg\|alt=Fig 2. Sliding Pair\|thumb\|Fig 2. Sliding Pair]]
	#*Turning pair - Kinematic pair where one link has a turning motion relative to the other. In fig 1. link 2 is having a turning motion relative to link 1, hence links 2 and 1 constitutes turning pair. Similarly links 3 & 4 and 2 & 3 forms turning pair.		#*Turning pair - Kinematic pair where one link has a turning motion relative to the other. In fig 1. link 2 is having a turning motion relative to link 1, hence links 2 and 1 constitutes turning pair. Similarly links 3 & 4 and 2 & 3 forms turning pair.
	#*Rolling pair - Kinematic pair where one link has a rolling motion relative to the other. Example: A rolling wheel on a flat surface forms a rolling pair. In a ball bearing , the ball and bearing forms one rolling pair and other rolling pair is ball and the shaft.		#*Rolling pair - Kinematic pair where one link has a rolling motion relative to the other. Example: A rolling wheel on a flat surface forms a rolling pair. In a ball bearing , the ball and bearing forms one rolling pair and other rolling pair is ball and the shaft.
	#*[[File:Screw Pair.jpg\|alt=Fig 3. Screw Pair\|thumb\|Fig 3. Screw Pair]]~~Screw pair ( Helical pair) - Kinematic pair where the two links have a turning as well~~ as sliding motion between them. The lead screw and the nut of a lathe is a screw pair. Fig 3 shows screw pair.		#*Screw pair ( Helical pair) - Kinematic pair where the two links have a turning as well [[File:Screw Pair.jpg\|alt=Fig 3. Screw Pair\|thumb\|Fig 3. Screw Pair]]as sliding motion between them. The lead screw and the nut of a lathe is a screw pair. Fig 3 shows screw pair.
	#*Spherical pair - Kinematic pair where one link in the form of sphere turns inside a fixed link. Ball and socket joint shown in fig 4. is a spherical pair.		#*Spherical pair - Kinematic pair where one link in the form of sphere turns inside a fixed link. Ball and socket joint shown in fig 4. is a spherical pair.[[File:Ball and Socket Joint.jpg\|alt=Fig 4. Ball & Socket Joint\|thumb\|Fig 4. Ball & Socket Joint]]
	#According to the nature of mechanical constraint between two links		#According to the nature of mechanical constraint between two links
	#*Closed pair - Two elements of the pair are held together mechanically		#*Closed pair - Two elements of the pair are held together mechanically
	#*Unclosed pair - Two elements of the pair are in contact due to force of gravity or due to some spring action . Example Cam and the follower in fig. 5 as it is kept in contact by the forces exerted by spring and gravity.		#*Unclosed pair - Two elements of the pair are in contact due to force of gravity or due to some spring action . Example Cam and the follower in fig. 5 as it is kept in contact by the forces exerted by spring and gravity.[[File:Cam & Follower.jpg\|alt=Fig 5. Cam & Follower\|thumb\|Fig 5. Cam & Follower]]
	=== Degrees of Freedom ===		=== Degrees of Freedom ===
	The number of independent motion (translation and rotational) a body can have is known as Degrees of freedom.<ref>{{Cite web\|title=Basic Kinematics of constrained rigid bodies\|url=https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt4.html}}</ref>		The number of independent motion (translation and rotational) a body can have is known as Degrees of freedom.<ref>{{Cite web\|title=Basic Kinematics of constrained rigid bodies\|url=https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt4.html}}</ref>
			[[File:Degrees of Freedom.jpg\|alt=Fig 6. Degrees of Freedom\|thumb\|Fig 6. Degrees of Freedom]]
	Fig 6. shows a rigid body in a space. If there is no constraint on the body then the following independent motion can be described.		Fig 6. shows a rigid body in a space. If there is no constraint on the body then the following independent motion can be described.

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	Hence the body can have six independent motions. This body is said to have six degrees of freedom.		Hence the body can have six independent motions. This body is said to have six degrees of freedom.

	Degrees of freedom = 6 - number of constraints if number of constraints are four then degrees of freedom = 6 - 4 = 2		Degrees of freedom = 6 - number of constraints

			if number of constraints are four then degrees of freedom = 6 - 4 = 2

	=== Kinematic Chain ===		=== Kinematic Chain ===
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	<math>j = \frac{3}{2} L -2</math> .................... (1.2)		<math>j = \frac{3}{2} L -2</math> .................... (1.2)

	The equations (1.1) and (1.2) are applied only to kinematic chains having lower pairs. If they are applied to kinematic chains having ~~higher~~ pairs, then each higher pair must be taken equivalent to two lower pairs and an additional link. In equations (1.1) and (1.2) if		The equations (1.1) and (1.2) are applied only to kinematic chains having lower pairs. If they are applied to kinematic chains having

			L.H.S = R.H.S then chain is constrainedhigher pairs, then each higher pair must be taken equivalent to two lower pairs and an additional link. In equations (1.1) and (1.2) if

	L.H.S > R.H.S then chain is locked		L.H.S > R.H.S then chain is locked

	~~L.H.S = R.H.S then chain is constrained~~

	L.H.S < R.H.S then chain is unconstrained		L.H.S < R.H.S then chain is unconstrained
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	[[Category:Mechanical engineering]]		[[Category:Mechanical engineering]]
	<references />		<references />
	~~[[File:Ball Socket joint.png\|alt=Ball and Socket Joint\|thumb\|Fig 4. Ball and Socket Joint]]~~
	~~[[File:Fig 4. Spherical pair.png\|alt=Spherical pair\|thumb\|Fig 5. Cam & follower]]~~

alpha>Ramamurthy S: Images updated

2022-09-23T08:05:09Z

Images updated

alpha>Ramamurthy S: /* Kinematic Pair */

2022-09-19T06:39:20Z

Kinematic Pair

← Older revision		Revision as of 12:09, 19 September 2022
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	=== Kinematic Pair ===		=== Kinematic Pair ===
	[[File:Image0609.png\|alt=image0609\|thumb\|Fig 1. Slider Crank Mechanism]]		[[File:Image0609.png\|alt=image0609\|thumb\|Fig 1. Slider Crank Mechanism]]
	Kinematic pair is ~~a joint of~~ two links ~~having~~ relative motion between them. In a slider crank mechanism shown in fig 1. here are the Kinematic pairs .		Kinematic pair is defined as the two links or elements of a machine when in contact with each other are said to form a pair. If the relative motion between them is completely or successfully constrained in a definite direction, the pair is known as the Kinematic pair.<ref>{{Cite web\|title=Kinematic Pair\|url=https://learnmechanical.com/kinematic-pair/}}</ref>

			In a slider crank mechanism shown in fig 1. here are the Kinematic pairs .

	* Link 2 rotates relative to link 1 and hence link 1 and 2 is a Kinematic pair.		* Link 2 rotates relative to link 1 and hence link 1 and 2 is a Kinematic pair.

alpha>Ramamurthy S: Citation added

2022-09-19T06:28:03Z

Citation added

← Older revision		Revision as of 11:58, 19 September 2022
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	== Definition ==		== Definition ==
	Theory of Machines is a branch of science dealing with the study of relative motion between the various parts of a machine and forces which act on them. Theory of Machines has two sub branches namely Kinematics and Dynamics.		Theory of Machines is a branch of science dealing with the study of relative motion between the various parts of a machine and forces which act on them.<ref>{{Cite book\|last=Bansal\|first=Dr. R. K.\|title=Theory of Machines\|pages=1}}</ref> Theory of Machines has two sub branches namely Kinematics and Dynamics.

	Kinematics deals with the study of relative motion between the various parts of a machine. The force which act on them would be static in nature.		Kinematics deals with the study of relative motion between the various parts of a machine. The force which act on them would be static in nature.
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	=== Degrees of Freedom ===		=== Degrees of Freedom ===
	The number of independent motion (translation and rotational) a body can have is known as Degrees of freedom.		The number of independent motion (translation and rotational) a body can have is known as Degrees of freedom.<ref>{{Cite web\|title=Basic Kinematics of constrained rigid bodies\|url=https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt4.html}}</ref>

	Fig 6. shows a rigid body in a space. If there is no constraint on the body then the following independent motion can be described.		Fig 6. shows a rigid body in a space. If there is no constraint on the body then the following independent motion can be described.

← Older revision		Revision as of 13:35, 23 September 2022
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	#*Higher Pair - Two links has a point or line of contact between them. Example: Wheel rolling on a surface and Cam & follower		#*Higher Pair - Two links has a point or line of contact between them. Example: Wheel rolling on a surface and Cam & follower
	#According to the type of relative motion between the two links		#According to the type of relative motion between the two links
	#*Sliding pair - Kinematic pair where the two links have a sliding motion relative to each other. Example : rectangle rod in a rectangular hole as shown in the fig 2 .		#*[[File:Sliding Pair.jpg\|alt=Fig 2. Sliding Pair\|thumb\|Fig 2. Sliding Pair]]Sliding pair - Kinematic pair where the two links have a sliding motion relative to each other. Example : rectangle rod in a rectangular hole as shown in the fig 2 .
	#*Turning pair - Kinematic pair where one link has a turning motion relative to the other. In fig 1. link 2 is having a turning motion relative to link 1, hence links 2 and 1 constitutes turning pair. Similarly links 3 & 4 and 2 & 3 forms turning pair.		#*Turning pair - Kinematic pair where one link has a turning motion relative to the other. In fig 1. link 2 is having a turning motion relative to link 1, hence links 2 and 1 constitutes turning pair. Similarly links 3 & 4 and 2 & 3 forms turning pair.
	#*Rolling pair - Kinematic pair where one link has a rolling motion relative to the other. Example: A rolling wheel on a flat surface forms a rolling pair. In a ball bearing , the ball and bearing forms one rolling pair and other rolling pair is ball and the shaft.		#*Rolling pair - Kinematic pair where one link has a rolling motion relative to the other. Example: A rolling wheel on a flat surface forms a rolling pair. In a ball bearing , the ball and bearing forms one rolling pair and other rolling pair is ball and the shaft.
	#*Screw pair ( Helical pair) - Kinematic pair where the two links have a turning as well as sliding motion between them. The lead screw and the nut of a lathe is a screw pair. Fig 3 shows screw pair.		#*[[File:Screw Pair.jpg\|alt=Fig 3. Screw Pair\|thumb\|Fig 3. Screw Pair]]Screw pair ( Helical pair) - Kinematic pair where the two links have a turning as well as sliding motion between them. The lead screw and the nut of a lathe is a screw pair. Fig 3 shows screw pair.
	#*Spherical pair - Kinematic pair where one link in the form of sphere turns inside a fixed link. Ball and socket joint shown in fig 4. is a spherical pair.		#*Spherical pair - Kinematic pair where one link in the form of sphere turns inside a fixed link. Ball and socket joint shown in fig 4. is a spherical pair.
	#According to the nature of mechanical constraint between two links		#According to the nature of mechanical constraint between two links
	#*Closed pair - Two elements of the pair are held together mechanically		#*Closed pair - Two elements of the pair are held together mechanically
	#*Unclosed pair - Two elements of the pair are in contact due to force of gravity or due to some spring action . Example Cam and the follower in fig. 5 as it is kept in contact by the forces exerted by spring and gravity.		#*Unclosed pair - Two elements of the pair are in contact due to force of gravity or due to some spring action . Example Cam and the follower in fig. 5 as it is kept in contact by the forces exerted by spring and gravity.
	~~[[File:Sliding Pair-1.png\|alt=Sliding Pair\|thumb\|Fig 2. Sliding Pair]]~~

	=== Degrees of Freedom ===		=== Degrees of Freedom ===
	The number of independent motion (translation and rotational) a body can have is known as Degrees of freedom.<ref>{{Cite web\|title=Basic Kinematics of constrained rigid bodies\|url=https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt4.html}}</ref>		The number of independent motion (translation and rotational) a body can have is known as Degrees of freedom.<ref>{{Cite web\|title=Basic Kinematics of constrained rigid bodies\|url=https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt4.html}}</ref>
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	[[Category:Mechanical engineering]]		[[Category:Mechanical engineering]]
	<references />		<references />
	~~[[File:Screw pair.png\|alt=Screw Pair\|thumb\|Fig 3. Screw Pair]]~~
	[[File:Ball Socket joint.png\|alt=Ball and Socket Joint\|thumb\|Fig 4. Ball and Socket Joint]]		[[File:Ball Socket joint.png\|alt=Ball and Socket Joint\|thumb\|Fig 4. Ball and Socket Joint]]
	[[File:Fig 4. Spherical pair.png\|alt=Spherical pair\|thumb\|Fig 5. Cam & follower]]		[[File:Fig 4. Spherical pair.png\|alt=Spherical pair\|thumb\|Fig 5. Cam & follower]]