An elliptical trammel (also known as the Trammel of Archimedes) is used to draw ellipses of various sizes. Elliptical Trammel is an inversion of a double slider crank chain in which there are two sliding pairs and two turning pairs. Slider 1 (Link 4) moves vertically while slider 2 (Link 2) moves horizontally.
The double slider crankshaft has two sliding pairs and two twist pairs. It is named the double slider crankshaft because it has two sliding pairs. It has two sliders, a frame in which the slider moves, and a link that connects the two slides and fixes the distance between the two sliders.
The Scotch yoke mechanism is a reciprocating motion mechanism, converting the linear motion of a slider into the rotational motion of a crank or vice versa. In the present study, it has been considered that the gravitational forces are perpendicular to the motion plane.
This mechanism is mostly used in shaping and slotting machines. In this mechanism, the link CD (link 2) forming the turning pair is fixed, as shown in Fig. Link 2 corresponds to a crank in a reciprocating steam engine. The driving crank CA (link 3) rotates at a uniform angular speed. The slider (link 4) attached to the crank pin at A slides along the slotted bar PA (link 1) which oscillates at a pivoted point D. The connecting rod PR carries the ram at R to which a cutting tool is fixed. The motion of the tool is constrained along the line RD produced, i.e. along a line passing through D and perpendicular to CD. from the position DP1 to DP2) through an angle α in the clockwise direction, the tool moves from the left-hand end of its stroke to the right-hand end through a distance 2 PD. Now when the driving crank moves from the position CA2 to CA1 (or the link DP from DP2 to DP1 ) through an angle β in the clockwise direction, the tool moves back from the right-hand end of its stroke to the left-hand end.
A slider-crank linkage is a four-link mechanism with three revolute joints and one prismatic, or sliding, joint. The rotation of the crank drives the linear movement the slider, or the expansion of gases against a sliding piston in a cylinder can drive the rotation of the crank.
An in-line crank slider is oriented in a way in which the pivot point of the crank is coincident with the axis of the linear movement. The follower arm, which is the link that connects the crank arm to the slider, connects to a pin in the center of sliding object. This pin is considered to be on the linear movement axis. Therefore, to be considered an in-line crank slider, the pivot point of the crank arm must be in-line with this pin point. The stroke((ΔR4)max) of an in-line crank slider is defined as the maximum linear distance the slider may travel between the two extreme points of its motion. With an in-line crank slider, the motion of the crank and follower links is symmetric about the sliding axis. This means that the crank angle required to execute a forward stroke is equivalent to the angle required to perform a reverse stroke. For this reason, the in-line slider-crank mechanism produces balanced motion. This balanced motion implies other ideas as well. Assuming the crank arm is driven at a constant velocity, the time it takes to perform a forward stroke is equal to the time it takes to perform a reverse stroke.
The graphical method of designing an in-line slider-crank mechanism involves the usage of hand-drawn or computerized diagrams. These diagrams are drawn to scale in order for easy evaluation and successful design. Basic trigonometry, the practice of analyzing the relationship between triangle features in order to determine any unknown values, can be used with a graphical compass and protractor alongside these diagrams to determine the required stroke or link lengths.
When the stroke of a mechanism needs to be calculated, first identify the ground level for the specified slider-crank mechanism. This ground level is the axis on which both the crank arm pivot-point and the slider pin are positioned. Draw the crank arm pivot point anywhere on this ground level. Once the pin positions are correctly placed, set a graphical compass to the given link length of the crank arm. Positioning the compass point on the pivot point of the crank arm, rotate the compass to produce a circle with radius equal to the length of the crank arm. This newly drawn circle represents the potential motion of the crank arm. Next, draw two models of the mechanism. These models will be oriented in a way that displays both the extreme positions of the slider. Once both diagrams are drawn, the linear distance between the retracted slider and the extended slider can be easily measured to determine the slider-crank stroke.
The retracted position of the slider is determined by further graphical evaluation. Now that the crank path is found, draw the crank slider arm in the position that places it as far away as possible from the slider. Once drawn, the crank arm should be coincident with the ground level axis that was initially drawn. Next, from the free point on the crank arm, draw the follower link using its measured or given length. Draw this length coincident with the ground level axis but in the direction toward the slider. The unhinged end of the follower will now be at the fully retracted position of the slider. Next, the extended position of the slider needs to be determined. From the pivot point of the crank arm, draw a new crank arm coincident with the ground level axis but in a position closest to the slider. This position should put the new crank arm at an angle of 180 degrees away from the retracted crank arm. Then draw the follower link with its given length in the same manner as previously mentioned. The unhinged point of the new follower will now be at the fully extended position of the slider.
To analytically design an in-line slider crank and achieve the desired stroke, the appropriate lengths of the two links, the crank and follower, need to be determined. For this case, the crank arm will be referred to as L2, and the follower link will be referred to as L3. With all in-line slider-crank mechanisms, the stroke is twice the length of the crank arm. Therefore, given the stroke, the length of the crank arm can be determined. This relationship is represented as:
The analytical method for designing an offset crank slider mechanism is the process by which triangular geometry is evaluated in order to determine generalized relationships among certain lengths, distances, and angles. These generalized relationships are displayed in the form of 3 equations and can be used to determine unknown values for almost any offset slider-crank. These equations express the link lengths, L1, L2, and L3, as a function of the stroke,(ΔR4)max, the imbalance angle, β, and the angle of an arbitrary line M, θM. Arbitrary line M is a designer-unique line that runs through the crank pivot point and the extreme retracted slider position. The 3 equations are as follows:
Slider-crank chain inversion arises when the connecting rod, or coupler, of a slider-crank linkage becomes the ground link, so the slider is connected directly to the crank. This inverted slider-crank is the form of a slider-crank linkage that is often used to actuate a hinged joint in construction equipment like a crane or backhoe, as well as to open and close a swinging gate or door.
A slider-crank is a four-bar linkage that has a crank that rotates coupled to a slider that the moves along a straight line. This mechanism is composed of three important parts: The crank which is the rotating disc, the slider which slides inside the tube and the connecting rod which joins the parts together. As the slider moves to the right the connecting rod pushes the wheel round for the first 180 degrees of wheel rotation. When the slider begins to move back into the tube, the connecting rod pulls the wheel round to complete the rotation.
Abstract:In a micro-manipulation system, the compliant gripper is used for gripping, handling and assembling of objects. Large displacement and anti-buckling characteristics are desired in the design of the gripper. In this paper, a compliant gripper with these two characteristics is proposed, modelled and verified. The large displacement is enabled by using distributed compliance in a double-slider kinematic mechanism. An inverted flexure arrangement enables the anti-buckling of the gripper when closing the two jaws. A pseudo-rigid-body model (PRBM) method with the help of virtual work principle is employed to obtain several desired analytical relations including the amplification coefficient and kinetostatics. The results of the finite element analysis (FEA) are shown to be consistent with the results of the derived analytical model. An experimental test was carried out through a milling machined aluminium alloy prototype, the results of which verify the good performance of the compliant gripper.Keywords: compliant gripper; large motion; anti-buckling; modelling
Slider crank chain: This is a kinematic chain having four links. It has one sliding pair and three turning pairs. Link 2 has rotary motion and is called crank. Link 3 has got combined rotary and reciprocating motion and is called connecting rod. Link 4 has reciprocating motion and is called slider. Link 1 is frame (fixed). This mechanism is used to convert rotary motion to reciprocating and vice versa.
Double slider crank chain is a four-bar kinematic chain having 2 sliding Pairs and 2 turning pairs such that two pairs of the same kind are adjacent. The general version of the double slider crank chain is shown in fig. 1. two Die-blocks, P & Q, slide along slots in a frame, and the pins P & Q on the Die-blocks are connected by a link PQ 2b1af7f3a8