Rotational Stiffness - Revision history

EricNickel: /* Rotational Stiffness */

2008-03-21T04:52:49Z

Rotational Stiffness

← Older revision		Revision as of 23:52, 20 March 2008
Line 158:		Line 158:


	T = k(rotational) * (theta + pi/9)		<math>T = k(rotational) * (theta + pi/9)</math>

EricNickel: /* Torque */

2008-03-21T04:52:22Z

Torque

← Older revision		Revision as of 23:52, 20 March 2008
Line 122:		Line 122:


	F = k * x (Hook's Law)		<math>F = k * x</math> (Hook's Law)

	T = F * d		<math>T = F * d</math>


Line 130:		Line 130:


	h = L2 * cos(theta)		<math>h = L2 * cos(theta)</math>

	a = L1 + L2 * sin(theta)		<math>a = L1 + L2 * sin(theta)</math>


Line 138:		Line 138:


	alpha = arctan(h/a)		<math>alpha = arctan(h/a)</math>

	beta = pi/2 - (theta + alpha)		<math>beta = pi/2 - (theta + alpha)</math>


Line 146:		Line 146:


	F(tangential) = k * (L3 - L3(initial)) * sin(beta)		<math>F(tangential) = k * (L3 - L3(initial)) * sin(beta)</math>

	T = F(tangential) * L2		<math>T = F(tangential) * L2</math>

EricNickel: /* Spring Extension */

2008-03-21T04:51:16Z

Spring Extension

← Older revision		Revision as of 23:51, 20 March 2008
Line 105:		Line 105:


	sqrt(h^2 + a^2)		<math>sqrt(h^2 + a^2)</math>

EricNickel: /* Torque/Moment */

2008-03-21T04:50:53Z

Torque/Moment

← Older revision		Revision as of 23:50, 20 March 2008
Line 37:		Line 37:


	T = F * d		<math>T = F * d</math>

EricNickel: /* Linear Spring */

2008-03-21T04:50:41Z

Linear Spring

← Older revision		Revision as of 23:50, 20 March 2008
Line 26:		Line 26:


	F = k * x		<math>F = k * x</math>

EricNickel: /* Stiffness */

2008-03-21T04:50:30Z

Stiffness

← Older revision		Revision as of 23:50, 20 March 2008
Line 13:		Line 13:


	T = k * theta		<math>T = k * theta</math>

EricNickel: /* Stiffness */

2008-03-21T04:50:12Z

Stiffness

← Older revision		Revision as of 23:50, 20 March 2008
Line 7:		Line 7:


	F = k * x		<math>F = k * x</math>

EricNickel: /* Rotational Stiffness */

2008-03-21T04:34:18Z

Rotational Stiffness

← Older revision		Revision as of 23:34, 20 March 2008
Line 154:		Line 154:

	===Rotational Stiffness===		===Rotational Stiffness===

			The rotational stiffness is the change in torque required to achieve a change in angle. Taken as a differential quantity, it is dT/d(theta). As the plots above show, the effect of changing angle on torque for a given L2 distance is approximately linear, therefore we assume a linear stiffness. This produces the following relationship for the joint:


			T = k(rotational) * (theta + pi/9)


			The spring is neutral at an angle of -pi/9, hence the constant in the above equation.


	<br clear=all>		<br clear=all>

EricNickel: /* Torque */

2008-03-21T04:27:18Z

Torque

← Older revision		Revision as of 23:27, 20 March 2008
Line 115:		Line 115:
	===Torque===		===Torque===
	[[Image:progstiffjointtorquecompdiag.jpg\|thumb\|200px\|Diagram showing the variables used to compute the torque applied by the spring\|right]]		[[Image:progstiffjointtorquecompdiag.jpg\|thumb\|200px\|Diagram showing the variables used to compute the torque applied by the spring\|right]]
	[[Image:~~progstiffjointloc2d~~.jpg\|thumb\|200px\|2D ~~plots~~ of the ~~height~~ ~~and~~ ~~lateral displacements of~~ the ~~rotating insertion point~~ for different angles and L2 distances\|right]]		[[Image:progstiffjointtorque3d.jpg\|thumb\|200px\|3D plot of the torque produced at the joint for different angles and L2 distances\|right]]
			[[Image:progstiffjointtorque2d.jpg\|thumb\|200px\|2D plots of the torque produced at the joint for different angles and L2 distances\|right]]


Line 142:		Line 143:


	The resulting torque is the tangential component of the tension force multiplied by the distance between the axis of rotation and the point of application of the force (L2).		The resulting torque is the tangential component of the tension force multiplied by the distance between the axis of rotation and the point of application of the force (L2). The stretch of the spring is L3 - L3(initial) and the spring has a linear stiffness k.


	F(tangential) = k *		F(tangential) = k * (L3 - L3(initial)) * sin(beta)

			T = F(tangential) * L2

EricNickel: /* Programmable Stiffness Joint */

2008-03-21T04:20:59Z

Programmable Stiffness Joint

← Older revision		Revision as of 23:20, 20 March 2008
Line 92:		Line 92:
	[[Image:progstiffjointloc3d.jpg\|thumb\|200px\|3D plots of the height and lateral displacements of the rotating insertion point for different angles and L2 distances\|right]]		[[Image:progstiffjointloc3d.jpg\|thumb\|200px\|3D plots of the height and lateral displacements of the rotating insertion point for different angles and L2 distances\|right]]
	[[Image:progstiffjointloc2d.jpg\|thumb\|200px\|2D plots of the height and lateral displacements of the rotating insertion point for different angles and L2 distances\|right]]		[[Image:progstiffjointloc2d.jpg\|thumb\|200px\|2D plots of the height and lateral displacements of the rotating insertion point for different angles and L2 distances\|right]]
			[[Image:progstiffjointstretch3d.jpg\|thumb\|200px\|3D plot of the spring stretch for different angles and L2 distances\|right]]
			[[Image:progstiffjointstretch2d.jpg\|thumb\|200px\|2D plot of the spring stretch for different angles and L2 distances\|right]]


Line 113:		Line 115:
	===Torque===		===Torque===
	[[Image:progstiffjointtorquecompdiag.jpg\|thumb\|200px\|Diagram showing the variables used to compute the torque applied by the spring\|right]]		[[Image:progstiffjointtorquecompdiag.jpg\|thumb\|200px\|Diagram showing the variables used to compute the torque applied by the spring\|right]]
			[[Image:progstiffjointloc2d.jpg\|thumb\|200px\|2D plots of the height and lateral displacements of the rotating insertion point for different angles and L2 distances\|right]]


	The amount of tension applied to the rotating insertion point is directly proportional to the amount of extension of the spring as a result of Hook's Law. This is the force applied to the rotating member, and a force applied to an object a distance away from its axis of rotation produces a torque or moment.		The amount of tension applied to the rotating insertion point is directly proportional to the amount of extension of the spring as a result of Hook's Law. This is the force applied to the rotating member, and a force applied to an object a distance away from its axis of rotation produces a torque or moment.