June 22, 2008
June 22, 2008
June 25, 2008
13.101.1 - 13.101.16
F ij = normal force applied on link j by link i Fi = frictional force applied on link (slider) i by the foundation (link 1) F ij = frictional force applied on link j by link i J i = polar moment-of-inertia of link i about its centroid Gi mi = mass of link i M = moment n = total number of links including the foundation (link 1) qi = inertia torque of link i = J i i n2 = rpm of link 2 (+ve if ccw, and ve if cw) Q i = external force on link i, if any Ri = length of link i Ri = position vector of link i T = input-/output- (external) torque Ti = resultant external torque on link i, if any va = velocity of joint, say, A vi = velocity of the centroid of link i All angular positions are measured from x-axis.
Analytical force (or kinetic or kinetostatic) analysis of mechanisms has always been one of the lengthy and time-consuming problems of mechanical engineering. In the past few decades, a number of methods have been developed for force analysis of frictionless mechanisms, but only a few researchers have embarked on frictional mechanisms due to its further complexity. The subject is still under research as no efficient and widely accepted method is yet available for this purpose, especially for teaching.
Lauw and Kinzel1 developed an interactive computer-aided force analysis program (PORKIN), which includes Coulomb friction as well. Muir and Neuman2 introduced a formulation for dynamic modeling of multibody robotic mechanisms incorporating friction (stiction, Coulomb, rolling and viscous friction), based on Newtonean dynamics, kinetics and the concept of force/torque propagation and frictional coupling at a joint, using extensive matrix-vector dynamics formulation to solve the systems of linear algebraic equation. Verriest3 developed a method for kinematics and dynamics of a highly structured special-purpose robot, where direction- Brost and 4 Mason described a graphical method for analyzing the motion of a rigid body subject to multiple frictional contacts in a plane. Kraus et al5 simulated the dynamic systems using rigid body model with rolling and sliding unilateral contacts for planar systems. Song et al6 employed a general model of contact compliance to derive stability criterion for planar mechanical systems with frictional contacts, introducing a smooth nonlinear f 7 friction where the Coulo investigated the effect of prismatic joint inertia on dynamics of planar kinematic chains with friction, using nt inertia on the dynamic parameters of planar mechanisms.
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