VELOCITY ANALYSIS ENT 348 MECHANICAL SYSTEM DESIGN KINEMATICS

VELOCITY ANALYSIS ENT 348 MECHANICAL SYSTEM DESIGN KINEMATICS AND DYNAMICS OF MACHINERY, 2 ND EDITION, ROBERT NORTON, 2013

INTRODUCTION • Position analysis is done and the next step is to determine the velocities of all links and points of interest in a mechanism. • By knowing the velocities, we can calculate the kinetic energy and link’s acceleration.

DEFINITION OF VELOCITY •

DEFINITION OF VELOCITY •

DEFINITION OF VELOCITY • Pivot A is moving • Velocity difference equation

DEFINITION OF VELOCITY • Relative velocity

GRAPHICAL VELOCITY ANALYSIS • • Line pp represent the direction of VB • Line qq represent the direction of VBA

GRAPHICAL VELOCITY ANALYSIS q VA p p VBA VB q

GRAPHICAL VELOCITY ANALYSIS • Next find VC r VA VCA r VC

ANGULAR VELOCITY RATIO The definition of effective link pairs is two lines, mutually parallel, draw through the fixed pivots and intersecting the coupler extended.

ANGULAR VELOCITY RATIO The definition of effective link pairs is two lines, mutually parallel, draw through the fixed pivots and intersecting the coupler extended.

ANALYTICAL SOLUTIONS FOR VELOCITY ANALYSIS • The fourbar pin-jointed linkage

ANALYTICAL SOLUTIONS FOR VELOCITY ANALYSIS The vector loop equation: R 2 + R 3 – R 4 – R 1 = 0

ANALYTICAL SOLUTIONS FOR VELOCITY ANALYSIS

ANALYTICAL SOLUTIONS FOR VELOCITY ANALYSIS

ANALYTICAL SOLUTIONS FOR VELOCITY ANALYSIS The vector loop equation: VA + VBA – VB = 0

EXAMPLE 6 -7 •

EXAMPLE 6 -7

ANALYTICAL SOLUTIONS FOR VELOCITY ANALYSIS • The fourbar crank slider

ANALYTICAL SOLUTIONS FOR VELOCITY ANALYSIS The vector loop equation: R 2 - R 3 – R 4 – R 1 = 0

ANALYTICAL SOLUTIONS FOR VELOCITY ANALYSIS

ANALYTICAL SOLUTIONS FOR VELOCITY ANALYSIS The vector loop equation: VA - VAB – VB = 0 VA = VB + VAB = 0 VAB = -VBA VB = VA + VBA

EXAMPLE 6 -8 •

VELOCITY OF SLIP • Sliding joint between two links and neither one is ground link

EXAMPLE 6. 5 • Graphical velocity analysis at a sliding joint