STRUCTURAL ANALYSIS, GEOMETRY AND STATICS OF A COACH UNFOLDING MECHANISM

Transcription

1 STRUTURL LYSIS, EOMETRY STTIS O O UOLI MEISM Ovidiu TOESU*, ătălina ROU ()**, Păun TOESU* *) ssociate Professor, Politehnica Universit of ucharest, oval@hotmail.com **) iolog, igh School of iurgiu, catalina_nan@ahoo.com bstract: Starting from the constructive scheme of the mechanism, the kinematic scheme is drawn in three distinct positions (folded, middle and unfolded). means of this scheme the mobilit of the mechanism is calculated and the structural-topological formula of it is obtained. In the last section of the paper an algorithm of geometric calculus has been elaborated, starting from a kinematic link articulated to the base, element which is considered the driving component. Kewords: coach unfolding mechanism, kinematic scheme, mobilit, static calculation.. eneral spects constructive scheme of a coach unfolding mechanism has been considered []. This scheme is in three distinct positions: folded when the coach is used as a coach (fig..) and unfolded when the coach becomes a bed (fig..). ig... onstructive scheme of the coach mechanism in folded position [] ccording to the constructive scheme of the coach mechanism in folded position (fig..) a curved shape of some kinematic elements configured as articulated bars, has been remarked. Two kinematic components as bars of the mechanism are articulated to the base (fied element) which is represented b the rigid rectangular frame of the coach (fig..). In the unfolded position with maimum etension (fig..) the mechanism is totall as one piece, since the contact with the floor of the last element of the kinematic chain is made. In order to facilitate the manual actuating of the mechanism from unfolded to folded position, a tensioned spring force is used. 8

2 Specificall to this unfolded position are two kinematic components of the mechanism that are articulated each other and end up into a lineated position one from the other in the horizontal position of the coach as bed (fig..). ig... onstructive scheme of the coach mechanism in unfolded position (maimum etension) for reconfiguring (transforming) into bed [] The two mattresses are one over the other in the folded position of the coach (fig..) but in the unfolded position the upper mattress is rotated in the vertical plane and ends up in a lineated position in respect to the lower mattress (fig..).. Topological and geometric structure of the reconfigurable mechanism Starting from the constructive scheme of the coach mechanism in middle position (fig..) the kinematic scheme (fig..), in which the kinematic elements and joints are smbolicall represented, has been drawn. The kinematic elements are numbered b rab figures (,,,..., ) and the kinematic joints are marked b Latin capital letters (,,,..., M, ). Since some kinematic elements (, ) are depicted as curved bars (fig..), these are represented in the kinematic scheme (fig..) as continuous straight lines and dashed lines too. 9

3 The mobilit of the planar mechanism with jointed bars has been calculated b the formula []: M n (.) In formula (.) the following parameter values have been used (fig..): n ; ;. M L K E a K ig... Kinematic scheme of the coach reconfigurable mechanism in bed-coach configuration (middle position) The outcome after the calculation b formula (.) is: M (.) onsidering the bar as driving element (actuator) articulated to the base, the structuraltopological formula of the motor mechanism is []: MM M(,) L(,) L(,) L(,) (.) In realit the driving element is bar through point M where the actuating force of the user for folding and unfolding the mechanism is applied. The folded position of the coach is represented in fig... M L ' K a K ig... Kinematic scheme of the coach mechanism in folded configuration E

4 In the unfolded position of the coach the point (end of bar ) touches the floor while on the bar is acting, as resistance force, the helical spring tension a which links the mobile point K of the bar to the fied point K (fig..). M L E K ' a * K ig... Kinematic scheme of the coach mechanism in unfolded position (bed configuration) In the unfolded position the end of the bar, represented b point, props on the end * of the bed-coach base (fig..).. Kinematic geometr of the coach reconfigurable mechanism means of these geometric parameters the angular positions of all kinematic elements of the mechanism, in one instantaneous random position, can be calculated (fig..). -bar contour (fig..) with oriented sides (according to the sketched angles) has been considered, and for which the following vector equation has been written [, ]: (.) If the position of the bar is imposed b φ angle, the vector equation (.) becomes: or l l l l (.) In this form the vector equation (.) is equivalent with two scalar equations: l cos l cos l l cos ; (.) l sin l sin l sin. (.) means of these equations the values of the angles φ and φ can be calculated (as <9 angles). M L φ φ α a K E φ φ φ K φ ig... Kinematic scheme showing the positioned components φ α

5 In this phase the coordinates of the points and have been calculated (fig..): cos( ); l l sin( ); (.) cos( ); l l sin( ); (.) means of E triangle the φ and φ angles have been calculated: l cos l cos ; (.) l sin l sin. (.8) In the net phase the analtical relations of the articulations and are (fig..): l cos ; l sin; (.9) cos( ); l l sin( ); (.) The angles φ and φ can be calculated b means of triangle (fig..): l cos l cos ; (.) l sin l sin. (.) The artesian coordinates of the point have the following aspects (fig..): cos( ); l l sin( ) (.) or the points M and the artesian coordinates have been deduced (fig..): M M cos( ); M M sin( ) ; (.) cos( ); sin( ). (.). Static calculus of the coach mechanism in unfolded position kinematic scheme of the coach mechanism in unfolded position (fig..,.), in which the point reaches the floor forming a superior kinematic joint, is considered. The mobilit of the mechanism in this etreme position (fig..) has been calculated b formula []: M n (.) analzing the kinematic scheme in this particular position (fig..), the following structure parameters have been identified: n ; ; means of formula (.) results: M (.) In this etreme position, in which the bars and are horizontal, the planar articulated mechanism becomes rigid, being a determined static planar sstem., p, p M L E K ' a K ig... Kinematic scheme of the coach mechanism in etreme unfolded position, p *

6 The eterior forces that act on this rigid kinematic chain are three: the elastic force r of the helical spring a (applied in the point K), the gravit force p of the person ling horizontall on the mattress (which lies on the bars and ) and the gravit force i of each bar. In this planar kinematic chain structure (with comple make-up) there were not been identified an determined static simple kinematic chains [] of tpe dadic, triadic, tetradic, etc. urther, each kinematic element has been isolated, introducing in each joint two components of the reaction force corresponding to coordinate aes (fig..). R R R R R R R R R R a) b) c) ig... Static balance of the bars, and Regarding the gravit force p (applied in three points) numerical values within da and da have been considered.. onclusions The coach reconfigurable mechanisms are, in most cases, planar linkages. Taking in consideration the width of coaches, these mechanisms are designed as double spatial structures operating in parallel planes. rom the stud of constructive solutions, presented in various patent documents, the kinematic structures are consisting of man articulated bars in comple geometric configurations. These mechanisms can be compared with the planar manipulators having staged kinematic chains and being manuall actuated b the last element. In the paper a constructive scheme of a planar manipulator-mechanism has been considered. The mobilit of it has been deduced b calculation, the outcome being equal b one. Starting from a certain element considered the driving component, an algorithm of angular displacement calculus of the kinematic elements, b using the analtical method of vector contours, has been presented. The paper ends with a calculus of the reaction forces applied in articulations according to two outer forces (the gravit force of the person which lies on the unfolded coach and the resistance force of a helical spring). References. ntonescu, P., ntonescu, O., Mechanisms and dnamics of the machines (in Romanian), Printech Press, ucharest, ;. ntonescu, O., ntonescu, P., Mechanisms and manipulators (in Romanian), Printech Press, ucharest, ; R R R R R R R R

7 . oblea,., Snthesis of a hospital bed lifting and tilting mechanism using advanced simulation techniques, ournal of Mech. and Manip., Vol., o., pp. -, ;. Strîmbeanu, M., naliza și sinteza mecanismelor folosite la mobila reconfigurabilă, Teza de doctorat,.