Definitions. Kinematics the study of constrained motion without regard to forces that cause that motion

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1 Notes_0_0 of efinitions Kinematics the stud of constrained motion without regard to forces that cause that motion namics the stud of how forces cause motion ausalit the relationship between cause and effect egrees-of-freedom (OF) of motion specific was in which a rigid bod or mechanical sstem ma move Kinematic joint a connection between two rigid bodies that restricts specific OF of motion in a reproducible manner ad (kinematic pair) a pair of rigid bodies connected b a kinematic joint Kinematic chain (loop) a sequence of dads Link a rigid bod in a kinematic chain inar link a link with two joint connections Ternar link - a link with three joint connections Open kinematic chain (loop) one that does not close back onto itself losed kinematic chain (loop) one that does close back onto itself Mechanism - a kinematic chain designed to transfer motion but not a significant amount of power Machine - a kinematic chain designed to transfer power Skeletal diagram a succinct schematic drawing of a kinematic chain Topolog connectivit analsis of a chain without regard to geometr Mobilit OF for a mechanism Instant center - unique point at which two objects in general planar motion have the same velocit

2 Notes_0_0 of Forward kinematics a) given motion across internal joints b) find motion of output links Inverse kinematics a) given motion of output links b) find motion across internal joints Forward dnamics a) given eternal forcing functions acting on a sstem b) find the resultant motion and internal forces Inverse dnamics a) given specified or measured motion of a sstem b) find internal forces and eternal forcing functions required to cause that motion

3 Notes_0_0 of Skeletal iagrams Use letters for points Use numbers for links - number ground link as Skeletal links represent geometr of joint connections but not actual shape inar link Ternar link lanar J joint - allows OF, restricts OF evolute () rismatic () ure rolling with no slip V = r ω lanar J joint - allows OF, restricts OF in-in-slot olling with slip (similar to pin in slot) V r ω

4 Notes_0_0 of Single loop, closed chains Four bar In-line slider crank Offset slider crank Inverted slider crank Single loop, open chain Two loop, closed chain E Human arm and hand obotic manipulator Track hoe Sewing machine oints ma eist on several links simultaneousl

5 Notes_0_0 of Mobilit mobilit - Kutzbach (general), Grubler (onl J joints) nl = number of links, nj = number of J joints, nj = number of J joints M = (nl-) - nj - nj nl=, nj=, M=0 nl=, nj=, M= nl=, nj=, M= Special geometr ma allow additional OF nl=, nj=, M=0 nl=, nj=, M=0

6 Notes_0_0 of Topolog Use blobs for links intersections are joints - do not tr to represent shape Four-bar Slider crank Inverted slider crank nl=, nj=7, M= onnectivit Use circle with one tick mark for each link connections are joints Four-bar Slider crank Inverted slider crank nl=, nj=7, M=, E,,,,, E

7 Notes_0_0 7 of Tracked Ecavator For the tracked ecavator shown below, identif the number of links (nl), OF joints (nj), OF joints (nj) and mobilit (M). nl nj (,) nj 0 M iagram the topolog of this mechanism. 0 9 p 8 7

8 Notes_0_0 8 of Wanzer Needle ar Wanzer needle bar mechanism is shown below. isk has two orthogonal offset slots and that guide slider blocks and. Fied slot guides slider block. The slider blocks are connected to rigid triangular link at revolutes E, F and G. Link translates and rotates. isk has pure rotation about fied revolute. Sliders and are long enough that the do not jam as the cross the intersection of slots and, and the are short enough that the do not collide. Identif the number of links (nl), OF joints (nj), OF joints (nj) and mobilit (M). nl nj 7 (,) nj 0 M iagram the topolog and connectivit of this mechanism. slot F,F F,F slot E,E E,E hidden under link E F G,G G,G G slot

9 Notes_0_0 9 of Grashof riterion Grashof's criterion provides a simple test to ascertain if an input link for a four bar mechanism can rotate freel through one complete revolution. The sum of the shortest and longest links cannot be greater than the sum of the remaining links if there is to be continuous relative rotation between two links. If the above condition is not met then onl rocking motion would be possible for an link Four inversions of a four bar linkage are shown below.grashof's law states that one of the links (generall the shortest link) will be able to rotate continuousl if the following condition is met... b (shortest link ) + c(longest link) < a + d

10 Notes_0_0 0 of river ad for Fied Ecursion of a ivoted Link with a Grashof rank-ocker θ lace a local coordinate frame at the pivot for the link. Select point along the link and compute local locations and for each given limit position θ and θ. ngular ecursion (θ-θ) must be less than 80. ompute displacement {d} of point and unit direction { û }. θ {d} cosθ sin θ cosθ sin θ { r } = { r } = { d} = { r } { r } d = norm{ d} { û} { d} / d =

11 Notes_0_0 of Use the link as the output rocker of a Grashof crank rocker four bar mechanism. rank center will fall along the line joining and. rank length will be one-half displacement d. n length L for the coupler ma be selected as long as it satisfies the Grashof criterion. Tpicall L = + work wells. rank center ma be placed on either side of the link. L L { r } = { r } (L ) { û} + L L { r } = { r } + (L ) { û}

A rigid body free to move in a reference frame will, in the general case, have complex motion, which is simultaneously a combination of rotation and

A rigid body free to move in a reference frame will, in the general case, have complex motion, which is simultaneously a combination of rotation and 050389 - Analtical Elements of Mechanisms Introduction. Degrees of Freedom he number of degrees of freedom (DOF) of a sstem is equal to the number of independent parameters (measurements) that are needed