CN1279504C - Teaching aid for demonstrating dynamic relations of instant center, pole trace, temporary axis and pole face in fixed point rotation of rigid body - Google Patents

Abstract

The present invention relates to a teaching aid for demonstrating dynamic relations of instant center, pole trace, a temporary axis and a pole face in fixed point rotation of a rigid body, which relates to a demonstrating teaching aid for the content of geostatics in physical teaching. Each polhode (2 to 3 to 1), (2 to 3 to 2) of the present invention are respectively rolled in a tangential way corresponding to each herpolhode (4 to 1), (4 to 2). Each speed perpendicular device (3) respectively slides on a left slide plate (1 to 1) and a right slide plate (1 to 2), which are orthogonal. Each of speed perpendiculars (3 to 1 to 1), (3 to 1 to 2) are respectively perpendicular to the speed direction of each speed perpendicular device (3) and are intersected at the tangent point part of each polhode and herpolhode, and the speed perpendiculars (3 to 1 to 1), (3 to 1 to 2) show each dynamic instant center in a sliding way. The connecting line of the dynamic instant center at each height part shows a dynamic instantaneous axis (3 to 1 to 4), a polhodeface (2 to 4) is rolled corresponding to a herpolhode (5) and is tangented to the instantaneous axis. The present invention has the advantages of novel design and clear structure. Besides, the dynamic relation of three-dimensional space position of the instantaneous center, the polhode, the herpolhode, the direction of the instantaneous axis, the polhode face and the herpolhode face can be vividly and iconically shown.

Description

The fixed point of rigid body instantaneous center of rotation, utmost point mark, instantaneous axis, pole-face dynamic relationship demonstration teaching aid

Technical field:

The present invention relates to a kind of demonstration teaching aid of rigid dynamics content in the physics teaching.

Background technology:

The fixed point of rigid body rotation is the emphasis difficult point content in the rigid dynamics, introduced the notion of instantaneous, utmost point mark, instantaneous axis, pole-face for describing Rigid Body in Rotation With, these point, line, surface have very vital role in describing the fixed point of rigid body rotation, but they all be cannot see and touch less than describing understanding by imagination, thus these notions to take out very much picture hard to understand.Instantaneous and utmost point mark notion is the basis of instantaneous axis and pole-face notion, exist inner link between them, thus set up that description is instantaneous, the image space-filling model of space dynamic relationship and it is demonstrated out for understanding good these notions and describing fixed point of rigid body and rotate significant mutually between the utmost point mark, instantaneous axis, pole-face with the lively image of teaching aid.The two-dimentional dynamic relationship of " demonstration teaching aid of dynamic relation in rigid body turning centrodes " in the 2nd phase of calendar year 2001 " Physical Experiment ", introduced instantaneous and utmost point mark in the time of can only demonstrating STUDY ON PLANE PARALLEL MOTION OF RIGID BODY and the three-dimensional space position dynamic relationship of instantaneous and utmost point mark can not demonstrate fixed point of rigid body and rotate the time.

Summary of the invention:

The objective of the invention is to develop a kind of fixed point of rigid body instantaneous center of rotation, utmost point mark, instantaneous axis, pole-face dynamic relationship demonstration teaching aid, it have modern design, space structure relation clear simple and clear, the drive connection harmony is easy to the demonstration operation flexibly, change the abstract image that is, can vivo demonstrate the characteristics of the three-dimensional space position dynamic relationship between instantaneous, polhode, herpolhode, instantaneous axis direction, itself surface, the space surface simultaneously.The present invention comprises three-dimensional slide plate 1, rotor of rigid body 2, speed vertical line device 3, herpolhode 4, space surface 5; Three-dimensional slide plate 1 is made up of left skateboard 1-1, right slide plate 1-2, base plate 1-3, left skateboard 1-1 and right slide plate 1-2 two planar quadrature are fixed together, base plate 1-3 and left skateboard 1-1 and right slide plate 1-2 pairwise orthogonal are fixed together, and are provided with taper pitting 1-3-1 on the base plate 1-3 at left skateboard 1-1 and right slide plate 1-2 angle of cut place; Rotor of rigid body 2 is that the quadrature xsect is semielliptical hemicone, by left axostylus axostyle 2-1, right axostylus axostyle 2-2, at least two polhodes are upper body utmost point mark 2-3-1, following polhode 2-3-2, straight-bar 2-5-1, straight line 2-5-2 forms, the two ends of upper body utmost point mark 2-3-1 are separately fixed at the top of left axostylus axostyle 2-1 and right axostylus axostyle 2-2, its two ends, below that following polhode 2-3-2 is arranged on upper body utmost point mark 2-3-1 are separately fixed on left axostylus axostyle 2-1 and the right axostylus axostyle 2-2, the upper end of straight-bar 2-5-1 is fixed on the downside of upper body utmost point mark 2-3-1, the lower end of straight-bar 2-5-1 is unsettled, left side axostylus axostyle 2-1 and right axostylus axostyle 2-2 are arranged on the hemicone both sides and intersect on two buses of forming V-shape, the intersection point of left side axostylus axostyle 2-1 and right axostylus axostyle 2-2 bottom is its hemicone summit 2-1-2, the upper end of straight line 2-5-2 is fixed on down the downside of polhode 2-3-2, the lower end of straight line 2-5-2 is fixed on the 2-1-2 of hemicone summit, straight-bar 2-5-1 and straight line 2-5-2 are corresponding up and down on same cone element of rotor of rigid body 2 half cone faces, upper body utmost point mark 2-3-1 and following polhode 2-3-2 are that the planar cross-sectional that intersects vertically with the rotor of rigid body 2 hemicone axis of cone or the boundary curve in curved surface cross section are shaped as the semiellipse curve shape, by upper body utmost point mark 2-3-1, following polhode 2-3-2, straight-bar 2-5-1, straight line 2-5-2, the half cone face of the rotor of rigid body 2 that hemicone summit 2-1-2 constitutes forms itself surface 2-4.Speed vertical line device 3 is by speed vertical line 3-1, rigidity thin flat plate 3-2, sleeve pipe 3-3, axostylus axostyle 3-4, U-shaped frame 3-5, axle sleeve 3-6 forms, sleeve pipe 3-3 outside surface is fixed on the rigidity thin flat plate 3-2, the both sides of sleeve pipe 3-3 are fixed with axostylus axostyle 3-4 respectively, the central axis of rigidity thin flat plate 3-2 and sleeve pipe 3-3 all parallel with axostylus axostyle 3-4 with the central axis of sleeve pipe 3-3 is perpendicular to axostylus axostyle 3-4, two axle sleeve 3-6 are separately positioned on place, the inboard two ends of U-shaped frame 3-5, two axle sleeve 3-6 on the outer end of two axostylus axostyle 3-4 and the U-shaped frame 3-5 are rotationally connected, and the lower end that speed vertical line 3-1 is fixed on U-shaped frame 3-5 keeps vertical with axostylus axostyle 3-4; Herpolhode 4 is that A herpolhode 4-1, B herpolhode 4-2 form by at least two herpolhodes; A herpolhode 4-1 is corresponding with position and the shape of upper body utmost point mark 2-3-1 and following polhode 2-3-2 respectively with B herpolhode 4-2, the left end of A herpolhode 4-1 is fixed on the left skateboard 1-1, the right-hand member of A herpolhode 4-1 is fixed on the right slide plate 1-2, B herpolhode 4-2 is located at the below of A herpolhode 4-1, the left end of B herpolhode 4-2 is fixed on the left skateboard 1-1, and the right-hand member of B herpolhode 4-2 is fixed on the right slide plate 1-2; Space surface 5 is the part taper, is formed by herpolhode 4, E straight-bar 5-1-1, F straight line 5-1-2, taper pitting 1-3-1; The upper end of E straight-bar 5-1-1 is fixed on the downside of A herpolhode 4-1, the lower end of E straight-bar 5-1-1 is unsettled, the upper end of F straight line 5-1-2 is fixed on the downside of B herpolhode 4-2, the lower end of F straight line 5-1-2 is fixed on the taper pitting 1-3-1 on the base plate 1-3 of summit place of cone space pole-face 5, and E straight-bar 5-1-1 and F straight line 5-1-2 are corresponding up and down on same cone element of space surface 5; Rotor of rigid body 2 is arranged in the space that space surface 5 and left skateboard 1-1 and right slide plate 1-2 surround, the hemicone summit 2-1-2 of rotor of rigid body 2 places the taper pitting 1-3-1 on the base plate 1-3 interior as rotating fixed point, each speed vertical line device 3 is enclosed within respectively on the left axostylus axostyle 2-1 at place, two ends on upper body utmost point mark 2-3-1 and the following polhode 2-3-2 and the right axostylus axostyle 2-2 and with it by its sleeve pipe 3-3 and is rotationally connected, the speed vertical line 3-1 that is enclosed within on the speed vertical line device 3 on the left axostylus axostyle 2-1 is left speed vertical line 3-1-1, the speed vertical line 3-1 that is enclosed within on the speed vertical line device 3 on the right axostylus axostyle 2-2 is right speed vertical line 3-1-2, each rigidity thin flat plate 3-2 respectively with left skateboard 1-1, right slide plate 1-2 inside surface overlaps and is slidingly connected with it, upper body utmost point mark 2-3-1 and A herpolhode 4-1, following polhode 2-3-2 and B herpolhode 4-2 keep homonymy tangent in each orientation respectively, each left speed vertical line 3-1-1 and each right speed vertical line 3-1-2 hang respectively at the place, point of contact of upper body utmost point mark 2-3-1 and A herpolhode 4-1, the instantaneous position 3-1-3 that represents two differing heights places is respectively intersected at place, the point of contact of following polhode 2-3-2 and B herpolhode 4-2, each instantaneous position 3-1-3 respectively with upper body utmost point mark 2-3-1 and A herpolhode 4-1, following polhode 2-3-2 and B herpolhode 4-2 are slidingly connected.The instantaneous position 3-1-3 of two differing heights is distributed in expression instantaneous axis direction 3-1-4 on the bus of tangent position between itself surface 2-4 and the space surface 5, and the lateral attitude of each E straight-bar 5-1-1, F straight line 5-1-2 on the space surface 5 distributes corresponding with the lateral attitude distribution of each straight-bar 2-5-1, straight line 2-5-2 on the itself surface 2-4.The left skateboard 1-1 of the three-dimensional slide plate 1 of the present invention, right slide plate 1-2, base plate 1-3 can be smooth sheet metal of rigidity or the smooth non-metal board of rigidity, left axostylus axostyle 2-1 on the rotor of rigid body 2, right axostylus axostyle 2-2, axostylus axostyle 3-4 on the speed vertical line device 3, sleeve pipe 3-3, U type frame 3-5 and axle sleeve 3-6, speed vertical line 3-1 can be rigid metallic material or rigidity nonmetallic materials, upper body utmost point mark 2-3-1, following polhode 2-3-2, A herpolhode 4-1, B herpolhode 4-2 can bend to the rigidity curve with tinsel, rigidity thin flat plate 3-2, straight-bar 2-5-1, straight line 2-5-2, E straight-bar 5-1-1, F straight line 5-1-2 can be that rigid metallic material or rigidity nonmetallic materials are made, and the connection between each parts can be glued together or weld fixing.The present invention has modern design, the space structure relation is clear simple and clear, the drive connection harmony is easy to demonstration, easy to operate flexibly, the method of abstract theory with image showed, can demonstrate simultaneously instantaneous, polhode, herpolhode, instantaneous axis direction, itself surface, the advantage of the three-dimensional space position dynamic relationship between the space surface vividly.

Description of drawings:

Fig. 1 is an one-piece construction synoptic diagram of the present invention, Fig. 2 is the structural representation of three-dimensional slide plate 1, Fig. 3 is the structural representation of rotor of rigid body 2, Fig. 4 is the structural representation of speed vertical line device 3, Fig. 5 is the structural representation of herpolhode 4, and Fig. 6 is the distribution schematic diagram of space surface 5, and Fig. 7 is the structural representation of embodiment two, Fig. 8 is the structural representation of embodiment three, and Fig. 9 is the structural representation of embodiment four.

Embodiment:

Embodiment one: (see that Fig. 1-Fig. 6) present embodiment is made up of three-dimensional slide plate 1, rotor of rigid body 2, speed vertical line device 3, herpolhode 4, space surface 5; Three-dimensional slide plate 1 is made up of left skateboard 1-1, right slide plate 1-2, base plate 1-3, left skateboard 1-1 and right slide plate 1-2 two planar quadrature are fixed together, base plate 1-3 and left skateboard 1-1 and right slide plate 1-2 pairwise orthogonal are fixed together, and are provided with taper pitting 1-3-1 on the base plate 1-3 at left skateboard 1-1 and right slide plate 1-2 angle of cut place; Rotor of rigid body 2 is that the quadrature xsect is semielliptical hemicone, by left axostylus axostyle 2-1, right axostylus axostyle 2-2, upper body utmost point mark 2-3-1, following polhode 2-3-2, straight-bar 2-5-1, straight line 2-5-2 forms, the two ends of upper body utmost point mark 2-3-1 are separately fixed at the top of left axostylus axostyle 2-1 and right axostylus axostyle 2-2, its two ends, below that following polhode 2-3-2 is arranged on upper body utmost point mark 2-3-1 are separately fixed on left axostylus axostyle 2-1 and the right axostylus axostyle 2-2, the upper end of straight-bar 2-5-1 is fixed on the downside of upper body utmost point mark 2-3-1, the lower end of straight-bar 2-5-1 is unsettled, left side axostylus axostyle 2-1 and right axostylus axostyle 2-2 are arranged on the hemicone both sides and intersect on two buses of forming V-shape, the intersection point of left side axostylus axostyle 2-1 and right axostylus axostyle 2-2 bottom is its hemicone summit 2-1-2, the upper end of straight line 2-5-2 is fixed on down the downside of polhode 2-3-2, the lower end of straight line 2-5-2 is fixed on the 2-1-2 of hemicone summit, straight-bar 2-5-1 and straight line 2-5-2 are corresponding up and down on same cone element of rotor of rigid body 2 half cone faces, upper body utmost point mark 2-3-1 and following polhode 2-3-2 are that the planar cross-sectional that intersects vertically with the rotor of rigid body 2 hemicone axis of cone or the boundary curve in curved surface cross section are shaped as the semiellipse curve shape, by upper body utmost point mark 2-3-1, following polhode 2-3-2, straight-bar 2-5-1, straight line 2-5-2, the half cone face of the rotor of rigid body 2 that hemicone summit 2-1-2 constitutes forms itself surface 2-4.Speed vertical line device 3 is by speed vertical line 3-1, rigidity thin flat plate 3-2, sleeve pipe 3-3, axostylus axostyle 3-4, U-shaped frame 3-5, axle sleeve 3-6 forms, sleeve pipe 3-3 outside surface is fixed on the rigidity thin flat plate 3-2, the both sides of sleeve pipe 3-3 are fixed with axostylus axostyle 3-4 respectively, the central axis of rigidity thin flat plate 3-2 and sleeve pipe 3-3 all parallel with axostylus axostyle 3-4 with the central axis of sleeve pipe 3-3 is perpendicular to axostylus axostyle 3-4, two axle sleeve 3-6 are separately positioned on place, the inboard two ends of U-shaped frame 3-5, two axle sleeve 3-6 on the outer end of two axostylus axostyle 3-4 and the U-shaped frame 3-5 are rotationally connected, and the lower end that speed vertical line 3-1 is fixed on U-shaped frame 3-5 keeps vertical with axostylus axostyle 3-4; Herpolhode 4 is made up of A herpolhode 4-1, B herpolhode 4-2; A herpolhode 4-1 is corresponding with position and the shape of upper body utmost point mark 2-3-1 and following polhode 2-3-2 respectively with B herpolhode 4-2, the left end of A herpolhode 4-1 is fixed on the left skateboard 1-1, the right-hand member of A herpolhode 4-1 is fixed on the right slide plate 1-2, B herpolhode 4-2 is located at the below of A herpolhode 4-1, the left end of B herpolhode 4-2 is fixed on the left skateboard 1-1, and the right-hand member of B herpolhode 4-2 is fixed on the right slide plate 1-2; Space surface 5 is the part taper, is formed by herpolhode 4, E straight-bar 5-1-1, F straight line 5-1-2, taper pitting 1-3-1.The upper end of E straight-bar 5-1-1 is fixed on the downside of A herpolhode 4-1, the lower end of E straight-bar 5-1-1 is unsettled, the upper end of F straight line 5-1-2 is fixed on the downside of B herpolhode 4-2, the lower end of F straight line 5-1-2 is fixed on the taper pitting 1-3-1 on the base plate 1-3 of summit place of cone space pole-face 5, and E straight-bar 5-1-1 and F straight line 5-1-2 are corresponding up and down on same cone element of space surface 5; Rotor of rigid body 2 is arranged in the space that space surface 5 and left skateboard 1-1 and right slide plate 1-2 surround, the hemicone summit 2-1-2 of rotor of rigid body 2 places the taper pitting 1-3-1 on the base plate 1-3 interior as rotating fixed point, each speed vertical line device 3 is enclosed within respectively on the left axostylus axostyle 2-1 at place, two ends on upper body utmost point mark 2-3-1 and the following polhode 2-3-2 and the right axostylus axostyle 2-2 and with it by its sleeve pipe 3-3 and is rotationally connected, the speed vertical line 3-1 that is enclosed within on the speed vertical line device 3 on the left axostylus axostyle 2-1 is left speed vertical line 3-1-1, the speed vertical line 3-1 that is enclosed within on the speed vertical line device 3 on the right axostylus axostyle 2-2 is right speed vertical line 3-1-2, each rigidity thin flat plate 3-2 respectively with left skateboard 1-1, right slide plate 1-2 inside surface overlaps and is slidingly connected with it, upper body utmost point mark 2-3-1 and A herpolhode 4-1, following polhode 2-3-2 and B herpolhode 4-2 keep homonymy tangent in each orientation respectively, each left speed vertical line 3-1-1 and each right speed vertical line 3-1-2 hang respectively at the place, point of contact of upper body utmost point mark 2-3-1 and A herpolhode 4-1, the instantaneous position 3-1-3 that represents two differing heights places is respectively intersected at place, the point of contact of following polhode 2-3-2 and B herpolhode 4-2, each instantaneous position 3-1-3 respectively with upper body utmost point mark 2-3-1 and A herpolhode 4-1, following polhode 2-3-2 and B herpolhode 4-2 are slidingly connected.The instantaneous position 3-1-3 of two differing heights is distributed in expression instantaneous axis direction 3-1-4 on the bus of tangent position between itself surface 2-4 and the space surface 5, and the lateral attitude of each E straight-bar 5-1-1, F straight line 5-1-2 on the space surface 5 distributes corresponding with the lateral attitude distribution of each straight-bar 2-5-1, straight line 2-5-2 on the itself surface 2-4.

Embodiment two: the difference of (see figure 7) present embodiment and embodiment one is, straight-bar 2-5-1 on the rotor of rigid body 2 on the cone element and straight line 2-5-2 are by transparent panel itself surface 2-4 ' replacement, E straight-bar 5-1-1 on space surface 5 cone elements and F straight line 5-1-2 are by transparent panel space surface 5 ' replacement, have transverse slot mouth 2-3-2-1 on the transparent panel itself surface 2-4 ' of the following polhode 2-3-2 position that laterally moves through in left speed vertical line 3-1-1 and right speed vertical line 3-1-2 point of crossing, transparent panel space surface 5 ' on B herpolhode 4-2 position have transverse slot mouth 4-2-1, so that left speed vertical line 3-1-1 that intersects and right speed vertical line 3-1-2 can laterally move in slit aperture, lateral separation at least five the lines 2-5-3 that draw equably on the bus of transparent panel itself surface 2-4 ', transparent panel space surface 5 ' bus on lateral separation at least five the lines 5-1-3 that draw equably.When rotor of rigid body 2 is in each orientation successively, transparent panel itself surface 2-4 ' and transparent panel space surface 5 ' on the lateral attitude of lines 2-5-3,5-1-3 at each bus place distribute one by one that correspondence overlaps the direction at instantaneous axis 3-1-4 respectively successively.Owing to increased the bar number of vertical element 2-5-3,5-1-3 on rotor of rigid body 2 and space surface 5 each cone element, thereby increased rotor of rigid body 2 in each orientation the number of times by these vertical elements demonstration instantaneous axis directions 3-1-4, make demonstration that instantaneous axis direction 3-1-4 changes near continuously.Other composition is identical with embodiment one with annexation.Transparent panel itself surface 2-4 ' and transparent panel space surface 5 ' can make by poly (methyl methacrylate) plate, transparent plastic sheet or transparent film.

Embodiment three: the difference of (see figure 8) present embodiment and embodiment one is, by straight-bar 2-5-1 and the straight line 2-5-2 on next number polhode 2-3-3 that increases and the following No. two polhode 2-3-4 replacement rotor of rigid body 2, and increase E straight-bar 5-1-1 and the F straight line 5-1-2 that has on C herpolhode 4-3 and the D herpolhode 4-4 replacement space surface 5; Next number polhode 2-3-3 is located at down the downside of polhode 2-3-2, its two ends are separately fixed on left axostylus axostyle 2-1 and the right axostylus axostyle 2-2, following No. two polhode 2-3-4 are located at the downside of next number polhode 2-3-3, its two ends are separately fixed on left axostylus axostyle 2-1 and the right axostylus axostyle 2-2, C herpolhode 4-3 is located at the downside of B herpolhode 4-2, its two ends are separately fixed on left skateboard 1-1 and the right slide plate 1-2, D herpolhode 4-4 is located at the downside of C herpolhode 4-3, its two ends are separately fixed on left skateboard 1-1 and the right slide plate 1-2, and the left axostylus axostyle 2-1 and the right axostylus axostyle 2-2 at place, two ends are provided with speed vertical line device 3 on next of Zeng Jiaing number polhode 2-3-3 and the following No. two polhode 2-3-4 respectively.Other composition is identical with embodiment one with annexation.Each represents each instantaneous position 3-1-3 to the left speed vertical line 3-1-1 and the intersection point of right speed vertical line 3-1-2 on the points of tangency of each polhode 2-3-1,2-3-2,2-3-3,2-3-4 and each herpolhode 4-1,4-2,4-3,4-4 of speed vertical line device 3, instantaneous position 3-1-3 of each height is distributed on the bus at tangent position place of itself surface 2-4 and space surface 5, can significantly present a dynamic approximate continuity straight line and represent instantaneous axis direction 3-1-4.

Embodiment four: the difference of (see figure 9) present embodiment and embodiment one is, the shape of the B herpolhode 4-2 on the following polhode 2-3-2 on the rotor of rigid body 2 and space surface 5 conical surfaces is respectively the edge line shape with rotor of rigid body 2 half cone faces and space surface 5 part conical surface surface of intersection cross sections.The instantaneous position 3-1-3 that left side speed vertical line 3-1-1 and right speed vertical line 3-1-2 point of crossing are represented each position that laterally is slidingly connected on following polhode 2-3-2 and B herpolhode 4-2 can be in the proper range fluctuations.Other composition is identical with embodiment one with annexation.

Principle of work: left axostylus axostyle 2-1, the right axostylus axostyle 2-2 of rotor of rigid body 2 both sides of rotating with two hand control fixed points are pressing each speed vertical line device 3 that it is slided along circular arc line around fixed point 1-3-1 in left skateboard 1-1, right slide plate 1-2 plane respectively, central point representation speed vertical line device 3 locas of each speed vertical line device 3 upper shaft lever 3-4, the tangential direction of its circular arc line of orientation of its axis of axostylus axostyle 3-4 is represented its movement velocity direction.On the rotor of rigid body 2 each highly on each aspect at place each of position, both sides each left speed vertical line 3-1-1 of speed vertical line device 3, right speed vertical line 3-1-2 are kept vertical with the movement velocity direction of each speed vertical line device 3 position, thereby each left speed vertical line 3-1-1, right speed vertical line 3-1-2 represent respectively highly to locate instantaneous position 3-1-3 at each intersection point highly.Because each rigidity thin flat plate 3-2 can rotate around left axostylus axostyle 2-1 and right axostylus axostyle 2-2 respectively by sleeve pipe 3-3, thereby each rigidity thin flat plate 3-2 can keep respectively inside surface with left skateboard 1-1 and right slide plate 1-2 heavily to be incorporated in sliding on its each inside surface to drive each left speed vertical line 3-1-1, the right speed vertical line 3-1-2 that intersects moved when rotor of rigid body 2 rotates, because each left speed vertical line 3-1-1, right speed vertical line 3-1-2 can rotate thereby can intersect the instantaneous position 3-1-3 that represents the arbitrary height place at the arbitrary height place around axostylus axostyle 3-4.The point of crossing that is distributed in left speed vertical line 3-1-1, right speed vertical line 3-1-2 that the upper body utmost point mark 2-3-1 at rotor of rigid body 2 differing heights places and following polhode 2-3-2 highly locate each respectively holds up has demonstrated the instantaneous position 3-1-3 at each differing heights place, along with rotor of rigid body 2 fixed points are rotated each and highly located instantaneous position 3-1-3 and move along upper body utmost point mark 2-3-1 and following polhode 2-3-2 respectively.The shape of upper body utmost point mark 2-3-1 and following polhode 2-3-2 all is crooked being made into of depicting in spatial movement according to each instantaneous position 3-1-3 of trajectory shape, and they all distribute on the conical surface of rotor of rigid body 2.For the oblique planar cross-sectional edge that intersects with rotor of rigid body 2 axis of cone out of plumb or the upper body utmost point mark 2-3-1 and the following polhode 2-3-2 of curved surface section edges shape, instantaneous position 3-1-3 thereon can be just in moving process or fluctuations.Upper body utmost point mark 2-3-1 on rotor of rigid body 2 and each cross section at following polhode 2-3-2 place not necessarily are parallel to each other, each cross section is plane not necessarily also, and therefore not only the rest frame of upper body utmost point mark 2-3-1 and the relative three-dimensional slide plate 1 of following polhode 2-3-2 is that body coordinate system on three-dimensional space curve but also the relative rotor of rigid body 2 also can be a three-dimensional space curve.This has just demonstrated the process of describing of three-dimensional space curve polhode on each aspect, upper body utmost point mark 2-3-1 and following polhode 2-3-2 on each aspect is distributed on the conical surface of rotor of rigid body 2 simultaneously, and this structure has also been demonstrated the relation of upper body utmost point mark 2-3-1 and following polhode 2-3-2 formation itself surface 2-4.

Instantaneous position 3-1-3 produces and each polhode position and corresponding each herpolhode 4 of shape by its shape of depicting each track at the track of depicting each instantaneous position 3-1-3 along upper body utmost point mark 2-3-1 and the three dimensions of also relative three-dimensional slide plate 1 when following polhode 2-3-2 moves on each aspect.Each herpolhode 4 and the common component part cone-shaped of the taper pitting 1-3-1 space surface 5 that rotates fixed point.Rotor of rigid body 2 fixed point is rotated and is made corresponding herpolhode 4 homonymies of each polhode and each be tangential on also relative rolling of instantaneous position 3-1-3, and this has just demonstrated the three dimensions dynamic relationship between instantaneous, polhode, the herpolhode.Tangent and the relative rolling of itself surface 2-4 simultaneously with space surface 5 homonymies, each is highly located instantaneous position 3-1-3 and is distributed in expression instantaneous axis direction 3-1-4 on the tangent line between itself surface 2-4 and the space surface 5, each bar bus of the itself surface 2-4 conical surface and each bar bus of space surface 5 conical surfaces coincide with instantaneous axis direction 3-1-4 successively, when each instantaneous position 3-1-3 moves to straight-bar 2-5-1, straight line 2-5-2 and E straight-bar 5-1-1, when F straight line 5-1-2 overlaps on the bus of position, these straight-bars and straight line can be significantly up and down each instantaneous position 3-1-3 be linked to be straight line and play the auxiliary effect of demonstrating instantaneous axis direction 3-1-4.Instantaneous axis direction 3-1-4 serves as to rotate fixed point to swing promptly simultaneously respectively along itself surface 2-4 and space surface 5 swings along each polhode and each herpolhode 4 respectively simultaneously in dynamically with rotor of rigid body 2 conical point 2-1-2.This has just demonstrated the dynamic relationship that is made of instantaneous axis instantaneous position, a plurality of differing heights place, demonstrated the dynamic relationship between instantaneous axis while and each aspect polhode and each the aspect herpolhode, demonstrate the dynamic relationship between instantaneous axis while and itself surface and the space surface, demonstrated the dynamic relationship between itself surface and the space surface.It is more that the lines of polhode and herpolhode increase, and the effect of its demonstration can be finer and smoother, vivider.

Claims (4)

1, the fixed point of rigid body instantaneous center of rotation, utmost point mark, instantaneous axis, pole-face dynamic relationship demonstration teaching aid, it comprises three-dimensional slide plate (1), rotor of rigid body (2), speed vertical line device (3), herpolhode (4), space surface (5); It is characterized in that three-dimensional slide plate (1) is made up of left skateboard (1-1), right slide plate (1-2), base plate (1-3), left skateboard (1-1) is fixed together with right slide plate (1-2) two planar quadrature, base plate (1-3) is fixed together with left skateboard (1-1) and right slide plate (1-2) pairwise orthogonal, is provided with taper pitting (1-3-1) on the base plate (1-3) at left skateboard (1-1) and right slide plate (1-2) angle of cut place; Rotor of rigid body (2) is that the quadrature xsect is semielliptical hemicone, by left axostylus axostyle (2-1), right axostylus axostyle (2-2), at least two polhodes are upper body utmost point mark (2-3-1), following polhode (2-3-2), straight-bar (2-5-1), straight line (2-5-2) is formed, the two ends of upper body utmost point mark (2-3-1) are separately fixed at the top of left axostylus axostyle (2-1) and right axostylus axostyle (2-2), its two ends, below that following polhode (2-3-2) is arranged on upper body utmost point mark (2-3-1) are separately fixed on left axostylus axostyle (2-1) and the right axostylus axostyle (2-2), the upper end of straight-bar (2-5-1) is fixed on the downside of upper body utmost point mark (2-3-1), the lower end of straight-bar (2-5-1) is unsettled, left side axostylus axostyle (2-1) and right axostylus axostyle (2-2) are arranged on the hemicone both sides and intersect on two buses of forming V-shape, the intersection point of left side axostylus axostyle (2-1) and right axostylus axostyle (2-2) bottom is its hemicone summit (2-1-2), the upper end of straight line (2-5-2) is fixed on down the downside of polhode (2-3-2), the lower end of straight line (2-5-2) is fixed on the hemicone summit (2-1-2), straight-bar (2-5-1) and straight line (2-5-2) are corresponding up and down on same cone element of rotor of rigid body (2) half cone face, upper body utmost point mark (2-3-1) and following polhode (2-3-2) are that the planar cross-sectional that intersects vertically with rotor of rigid body (2) the hemicone axis of cone or the boundary curve in curved surface cross section are shaped as the semiellipse curve shape, by upper body utmost point mark (2-3-1), following polhode (2-3-2), straight-bar (2-5-1), straight line (2-5-2), the half cone face of the rotor of rigid body (2) that hemicone summit (2-1-2) constitutes forms itself surface (2-4), speed vertical line device (3) is by speed vertical line (3-1), rigidity thin flat plate (3-2), sleeve pipe (3-3), axostylus axostyle (3-4), U-shaped frame (3-5), axle sleeve (3-6) is formed, the both sides that sleeve pipe (3-3) outside surface is fixed on rigidity thin flat plate (3-2) L sleeve pipe (3-3) are fixed with axostylus axostyle (3-4) respectively, the central axis of rigidity thin flat plate (3-2) and sleeve pipe (3-3) all parallel with axostylus axostyle (3-4) with the central axis of sleeve pipe (3-3) is perpendicular to axostylus axostyle (3-4), two axle sleeves (3-6) are separately positioned on place, the inboard two ends of U-shaped frame (3-5), two axle sleeves (3-6) on the outer end of two axostylus axostyles (3-4) and the U-shaped frame (3-5) are rotationally connected, and the lower end that speed vertical line (3-1) is fixed on U-shaped frame (3-5) keeps vertical with axostylus axostyle (3-4); Herpolhode (4) is that A herpolhode (4-1), B herpolhode (4-2) are formed by at least two herpolhodes; A herpolhode (4-1) is corresponding with the position and the shape of upper body utmost point mark (2-3-1) and following polhode (2-3-2) respectively with B herpolhode (4-2), the left end of A herpolhode (4-1) is fixed on the left skateboard (1-1), the right-hand member of A herpolhode (4-1) is fixed on the right slide plate (1-2), B herpolhode (4-2) is located at the below of A herpolhode (4-1), the left end of B herpolhode (4-2) is fixed on the left skateboard (1-1), and the right-hand member of B herpolhode (4-2) is fixed on the right slide plate (1-2); Space surface (5) is the part taper, by herpolhode (4), E straight-bar (5-1-1), F straight line (5-1-2), taper pitting (1-3-1) forms, the upper end of E straight-bar (5-1-1) is fixed on the downside of A herpolhode (4-1), the lower end of E straight-bar (5-1-1) is unsettled, the upper end of F straight line (5-1-2) is fixed on the downside of B herpolhode (4-2), the lower end of F straight line (5-1-2) is fixed on the taper pitting (1-3-1) on the summit place base plate (1-3) of cone space pole-face (5), E straight-bar (5-1-1) and F straight line (5-1-2) up and down correspondence on same cone element of space surface (5); Rotor of rigid body (2) is arranged in the space that space surface (5) and left skateboard (1-1) and right slide plate (1-2) surround, the hemicone summit (2-1-2) of rotor of rigid body (2) places the taper pitting (1-3-1) on the base plate (1-3) interior as rotating fixed point, each speed vertical line device (3) is enclosed within respectively on the left axostylus axostyle (2-1) at place, two ends on upper body utmost point mark (2-3-1) and the following polhode (2-3-2) and the right axostylus axostyle (2-2) and with it by its sleeve pipe (3-3) and is rotationally connected, the speed vertical line (3-1) that is enclosed within on the speed vertical line device (3) on the left axostylus axostyle (2-1) is a left speed vertical line (3-1-1), the speed vertical line (3-1) that is enclosed within on the speed vertical line device (3) on the right axostylus axostyle (2-2) is a right speed vertical line (3-1-2), each rigidity thin flat plate (3-2) respectively with left skateboard (1-1), right slide plate (1-2) inside surface overlaps and is slidingly connected with it, upper body utmost point mark (2-3-1) and A herpolhode (4-1), following polhode (2-3-2) keeps homonymy tangent in each orientation respectively with B herpolhode (4-2), each left speed vertical line (3-1-1) and each right speed vertical line (3-1-2) hang respectively at the point of contact place of upper body utmost point mark (2-3-1) with A herpolhode (4-1), following polhode (2-3-2) intersects the instantaneous position (3-1-3) of representing two differing heights places respectively with the place, point of contact of B herpolhode (4-2), each instantaneous position (3-1-3) respectively with upper body utmost point mark (2-3-1) and A herpolhode (4-1), following polhode (2-3-2) and B herpolhode (4-2) are slidingly connected, the instantaneous position (3-1-3) of two differing heights is distributed in expression instantaneous axis direction (3-1-4) on the bus of tangent position between itself surface (2-4) and the space surface (5), each the E straight-bar (5-1-1) on the space surface (5), the lateral attitude distribution of F straight line (5-1-2) and each straight-bar (2-5-1) on the itself surface (2-4), the lateral attitude of straight line (2-5-2) distributes corresponding.

2, the fixed point of rigid body instantaneous center of rotation according to claim 1, utmost point mark, instantaneous axis, pole-face dynamic relationship demonstration teaching aid, it is characterized in that straight-bar (2-5-1) and straight line (2-5-2) that rotor of rigid body (2) is gone up on the cone element are replaced by transparent panel itself surface (2-4 '), E straight-bar (5-1-1) on space surface (5) cone element and F straight line (5-1-2) are replaced by transparent panel space surface (5 '), have transverse slot mouth (2-3-2-1) on the transparent panel itself surface (2-4 ') of following polhode (2-3-2) position that laterally moves through in left speed vertical line (3-1-1) and right speed vertical line (3-1-2) point of crossing, go up B herpolhode (4-2) position at transparent panel space surface (5 ') and have transverse slot mouth (4-2-1), lateral separation at least five lines (2-5-3) that draw equably on the bus of transparent panel itself surface (2-4 '), lateral separation at least five lines (5-1-3) that draw equably on the bus of transparent panel space surface (5 ').

3, the fixed point of rigid body instantaneous center of rotation according to claim 1, utmost point mark, instantaneous axis, pole-face dynamic relationship demonstration teaching aid, it is characterized in that by straight-bar (2-5-1) and straight line (2-5-2) on next number polhode (2-3-3) that increases and following No. two polhodes (2-3-4) the replacement rotor of rigid body (2), and increase E straight-bar (5-1-1) and the F straight line (5-1-2) that has on C herpolhode (4-3) and D herpolhode (4-4) the replacement space surface (5); Next number polhode (2-3-3) is located at down the downside of polhode (2-3-2), its two ends are separately fixed on left axostylus axostyle (2-1) and the right axostylus axostyle (2-2), following No. two polhodes (2-3-4) are located at the downside of next number polhode (2-3-3), its two ends are separately fixed on left axostylus axostyle (2-1) and the right axostylus axostyle (2-2), C herpolhode (4-3) is located at the downside of B herpolhode (4-2), its two ends are separately fixed on left skateboard (1-1) and the right slide plate (1-2), D herpolhode (4-4) is located at the downside of C herpolhode (4-3), its two ends are separately fixed on left skateboard (1-1) and the right slide plate (1-2), and the left axostylus axostyle (2-1) and the right axostylus axostyle (2-2) at place, two ends are provided with speed vertical line device (3) on next of Zeng Jiaing number polhode (2-3-3) and following No. two polhodes (2-3-4) respectively.

4, the fixed point of rigid body instantaneous center of rotation according to claim 1, utmost point mark, instantaneous axis, pole-face dynamic relationship demonstration teaching aid, the shape that it is characterized in that following polhode (2-3-2) on the rotor of rigid body (2) and the B herpolhode (4-2) on space surface (5) conical surface are respectively the edge line shapes with rotor of rigid body (2) half cone face and space surface (5) part conical surface surface of intersection cross section.

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