CN113978165A

CN113978165A - Cycloid demonstration teaching aid that college mathematics teaching used

Info

Publication number: CN113978165A
Application number: CN202111287404.XA
Authority: CN
Inventors: 赵晓; 林悦馨; 薛雨昕; 郭祥; 陈俊
Original assignee: Fuzhou College of Foreign Studies and Trade
Current assignee: Fuzhou College of Foreign Studies and Trade
Priority date: 2021-11-02
Filing date: 2021-11-02
Publication date: 2022-01-28

Abstract

The invention discloses a cycloid demonstration teaching aid used for college mathematics teaching, which belongs to the technical field of teaching aids and comprises a bottom plate and a rotating shaft III, wherein two sides of the bottom plate are fixedly connected with side plates, a connecting plate I and a connecting plate II are fixedly connected between the two side plates together, a sliding block is slidably connected between the connecting plate I and the connecting plate II, the end part of the rotating shaft III is fixedly connected with a rotating disc, the end part of a fixing rod is fixedly connected with an air cylinder, the surface of the rotating shaft III is provided with a transmission part I for driving a piston to reciprocate, the cycloid demonstration teaching aid has the advantages that chalk is driven to horizontally move around the rotating shaft III by the rotation of the rotating shaft I, a figure is drawn on a blackboard, the drawn figure is accurate, students can understand the cycloid demonstration teaching aid more easily, the figure is not required to be drawn manually, the time is saved, the piston is driven to vertically reciprocate by the rotation of a cam, air is blown out from an air outlet pipe, and hard particles or dust on the surface of the blackboard is blown out, the effect of improving the quality of graphic demonstration and teaching.

Description

Cycloid demonstration teaching aid that college mathematics teaching used

Technical Field

The invention relates to the technical field of teaching aids, in particular to a cycloid demonstration teaching aid for college mathematics teaching.

Background

In university's mathematics teaching in-process, the teacher need be with the help of drawing instrument manual drawing on the blackboard in order to assist the teaching in order to understand textbook content for the convenience student, and manual drawing not only delays a large amount of times, and it is relatively poor to draw the precision in addition, makes the student produce the misunderstanding easily to the blackboard is owing to by frequent use, and the surface can be infected with stereoplasm granule or dust, and it is poor to lead to the teaching demonstration effect, has reduced teaching efficiency.

Disclosure of Invention

The invention aims to provide a cycloid demonstration teaching aid for university mathematics teaching, which is characterized in that a rotating shaft I rotates to drive a chalk to rotate around a rotating shaft III and simultaneously move in a translation mode, a graph is drawn on a blackboard, the drawn graph is accurate and can be easily understood by students, manual drawing is not needed, time is saved, a piston is driven to move up and down in a reciprocating mode through rotation of a cam, air is blown out of an air outlet pipe, hard particles or dust on the surface of the blackboard is blown away, the effect of graph demonstration and teaching quality is improved, the problems that a large amount of time is delayed, manual drawing accuracy is poor, the students are prone to misunderstanding, hard particles or dust can be stained on the surface of the blackboard due to frequent use, the teaching demonstration effect is poor, and the teaching efficiency is reduced are solved.

In order to achieve the purpose, the invention provides the following technical scheme: a cycloid demonstration teaching aid for college mathematics teaching comprises a base, a base plate and a third rotating shaft, wherein the base is fixedly connected with the base plate through a supporting column, side plates are fixedly connected with the two sides of the base plate, a first connecting plate and a second connecting plate are fixedly connected between the two side plates together, a first connecting plate and a second connecting plate are connected with each other in a sliding mode, an opening is formed in the surface of the slider, the third rotating shaft penetrates through the first connecting plate and is connected with the second connecting plate in a fixed-shaft rotating mode, a rotary disc is fixedly connected with the end portion of the third rotating shaft, chalk is installed on the surface of the rotary disc through a fixing part, a sliding opening is formed in the surface of the first connecting plate, the fixing rod penetrates through the sliding opening and is connected with the sliding opening in a sliding mode, an air cylinder is fixedly connected with the end portion of the fixing rod, an air inlet pipe and an air outlet pipe are respectively arranged on the side surface of the air cylinder, and a piston is slidably connected with the air cylinder, the surface of the rotating shaft III is provided with a first transmission part used for driving the piston to reciprocate, the upper surface of the bottom plate is fixedly connected with a supporting plate, the surface of the supporting plate is provided with a penetrating port used for the rotating shaft I to penetrate through and to be rotationally connected with a fixed shaft of the rotating shaft I, and the rotating shaft I is respectively provided with a second transmission part used for driving the sliding block to move in a translation manner and a third transmission part used for driving the rotating shaft to rotate.

Optionally, the transmission part II comprises a rotating shaft II, a first rotating plate is fixedly connected to the surface of the first rotating shaft, the end of the first rotating plate is sleeved on the surface of the second rotating shaft, a second rotating plate is rotatably connected to the surface of the second rotating shaft in a fixed-axis manner, a through hole used for allowing the third rotating shaft to penetrate and being rotatably connected with the fixed-axis of the third rotating plate is formed in the end of the surface of the second rotating plate, and a driving part used for driving the first rotating shaft to rotate is arranged on the supporting plate.

Optionally, transmission part three includes gear one, gear one fixed connection is in the surface of pivot one, the fixed surface of pivot two is connected with gear two, gear two with gear one meshes mutually, pivot two with be connected through belt drive mechanism transmission between the pivot three.

Optionally, one of the transmission parts comprises a cam, the cam is fixedly connected to the surface of the third rotating shaft, a piston rod is fixedly connected to the lower surface of the piston, the piston rod is abutted to the surface of the cam, a first spring is sleeved on the surface of the piston rod, and two ends of the first spring are respectively fixedly connected to the lower surface of the inflator and the surface of the piston rod.

Optionally, the fixed part includes rack plate and extrusion piece, the surface of carousel has been seted up and has been used for the rack plate with the recess that the extrusion piece stretched into, the side fixedly connected with spring two of rack plate, the tip of spring two with the inner wall fixed connection of recess, the side of extrusion piece seted up with the tooth's socket that the rack plate surface tooth was laminated mutually, the surface of extrusion piece is seted up and is used for the draw-in groove that the chalk stretched into, be provided with the clamping piece in the draw-in groove.

Optionally, the driving part includes a motor, the motor is fixedly mounted on the surface of the supporting plate, and an output end of the motor is fixedly connected with an end of the first rotating shaft.

Optionally, the upper surface fixed mounting of base has the storing box, the quantity of storing box is two to with the symmetric distribution, in order to put into the teaching aid in the storing box, convenient to use, the rational utilization space.

Optionally, the bottom of the base is provided with a universal wheel, and the base is fixed in position after being moved to a required position through the rolling property and the self-locking property of the universal wheel.

Compared with the prior art, the invention has the following beneficial effects:

according to the invention, the sliding block moves in a translation manner to drive the rotary table and the chalk to move in a translation manner, the rotary table is driven to rotate by rotating the rotary shaft I and rotating the rotary shaft III, and the chalk is driven to rotate around the rotary shaft III by rotating the rotary table, so that the chalk moves in a translation manner while rotating around the rotary shaft III, and the pattern is drawn on the blackboard.

The rotating shaft III rotates to drive the cam to rotate, the cam rotates to drive the piston rod to reciprocate up and down, the piston rod reciprocates up and down to drive the piston to reciprocate up and down, and air is blown out of the air outlet pipe, so that hard particles or dust on the surface of the blackboard is blown off, and the graphic demonstration effect and the teaching quality are improved.

The rack plate is driven to move by pressing the extrusion block downwards and matching the rack plate teeth with the extrusion block tooth grooves, so that the position of the extrusion block is adjusted, the chalk can draw different patterns, the change rule of the different patterns can be observed, and students can understand the patterns conveniently.

Drawings

FIG. 1 is a front view of the structure of the present invention;

FIG. 2 is a top view of the structure of the present invention;

FIG. 3 is a side cross-sectional view of the cartridge construction of the present invention;

FIG. 4 is a front view of the cam structure of the present invention;

fig. 5 is a front view of the turntable structure of the present invention.

In the figure: 1. a base; 2. a support pillar; 3. chalk; 4. a base plate; 5. a side plate; 6. a first connecting plate; 7. a second connecting plate; 8. a slider; 9. a support plate; 10. a first rotating shaft; 11. a motor; 12. a first gear; 13. a second gear; 14. a second rotating shaft; 15. rotating the first plate; 16. rotating a second plate; 17. a rotating shaft III; 18. a belt drive mechanism; 19. fixing the rod; 20. an air cylinder; 21. a cam; 22. a piston rod; 23. a piston; 24. an air outlet pipe; 25. a first spring; 26. a turntable; 27. a rack plate; 28. a groove; 29. a second spring; 30. extruding the block; 31. a card slot; 35. a storage box.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Referring to fig. 1 to 5, the present invention provides a technical solution: the utility model provides a cycloid demonstration teaching aid that university's mathematics teaching used, includes base 1, still includes bottom plate 4 and three 17 of pivot, base 1 with through support column 2 fixed connection between the bottom plate 4, the equal fixedly connected with curb plate 5 in both sides of bottom plate 4, two common fixedly connected with connecting plate 6 and connecting plate two 7 between the curb plate 5, sliding connection has slider 8 between connecting plate 6 and the connecting plate two 7, the surface of slider 8 is seted up and is used for the opening that three 17 of pivot passed and with it dead axle rotation is connected, the tip fixedly connected with carousel 26 of three 17 of pivot, chalk 3 is installed on the surface of carousel 26 through fixed part, the surface of connecting plate 6 is seted up and is used for dead lever 19 to pass and with its sliding connection's sliding opening 61, the tip fixedly connected with inflator 20 of dead lever 19, the side of the inflator 20 is respectively provided with an air inlet pipe and an air outlet pipe 24, the inflator 20 is connected with a piston 23 in a sliding manner, the surface of the rotating shaft III 17 is provided with a first transmission part used for driving the piston 23 to move back and forth, the upper surface of the bottom plate 4 is fixedly connected with a support plate 9, the surface of the support plate 9 is provided with a through hole used for the rotating shaft I10 to pass through and be connected with the rotating shaft III in a fixed shaft rotating manner, the rotating shaft I10 is respectively provided with a second transmission part used for driving the sliding block 8 to move in a translation manner and a third transmission part used for the rotating shaft III 17 to rotate, when in use, the chalk is fixed on the surface of the turntable 26 through the fixing part, then the device is moved, so that the chalk 3 is attached to the blackboard, the rotating shaft I10 is driven to rotate under the action of the driving part, and the rotating shaft III is driven to move in a translation manner and rotate under the action of the second transmission part and the third transmission part, rotate when moving through three 17 translations of pivot, drive carousel 26 and chalk 3 translation and move and rotate simultaneously to draw the figure on the blackboard, the figure of drawing is accurate, makes students understand more easily, and this equipment structure is simple, and the simple operation need not the manual drawing of mr, has saved the time, has improved teaching efficiency.

The piston 23 is driven to reciprocate up and down by the rotation of the third rotating shaft 17 and the action of the first transmission component, air is blown out from the air outlet pipe 24, so that hard particles or dust on the surface of the blackboard are blown off, and the graphic demonstration effect and the teaching quality are improved.

Further, the transmission part II comprises a rotating shaft II 14, the surface of the rotating shaft I10 is fixedly connected with a rotating plate I15, the end part of the rotating plate I15 is sleeved on the surface of the rotating shaft II 14, the surface of the rotating shaft II 14 is connected with a rotating plate II 16 in a rotating mode in a fixed axis mode, the end part of the surface of the rotating plate II 16 is provided with a through hole used for enabling the rotating shaft III 17 to penetrate through and be connected with the rotating shaft II in a fixed axis mode in a rotating mode, and a driving part used for driving the rotating shaft I10 to rotate is arranged on the supporting plate 9.

Further, the transmission component III comprises a gear I12, the gear I12 is fixedly connected to the surface of the rotating shaft I10, the surface of the rotating shaft II 14 is fixedly connected with a gear II 13, the gear II 13 is meshed with the gear I12, the rotating shaft II 14 is in transmission connection with the rotating shaft III 17 through a belt transmission mechanism 18, when the transmission component III is used, the gear I12 is driven to rotate through the rotation of the rotating shaft I10, the rotating shaft II 14 is driven to rotate around the rotating shaft I10 through the rotation of a rotating plate I15, the gear II 13 is further driven to rotate around the gear I12, the gear II 13 is driven through the self-rotation relation between the gear I12 and the gear II 13, the rotating shaft II 13 is driven to rotate through the self-rotation of the gear II 13, the rotating shaft II 14 is driven to rotate through the rotation of the rotating shaft II 14, the rotating shaft III 17 is driven to rotate under the action of the belt transmission mechanism 18, and the rotating shaft III 17 rotates through the rotation of the rotating shaft III 17, the rotating disc 26 is driven to rotate, the chalks 3 are driven to rotate around the third rotating shaft 17 through the rotation of the rotating disc 26, the chalks 3 move in a translation mode while rotating around the third rotating shaft 17, and therefore the patterns are drawn on the blackboard, and students can learn conveniently.

Further, one of the transmission parts includes a cam 21, the cam 21 is fixedly connected to the surface of the third rotating shaft 17, a piston rod 22 is fixedly connected to the lower surface of the piston 23, the piston rod 22 is abutted to the surface of the cam 21, a first spring 25 is sleeved on the surface of the piston rod 22, two ends of the first spring 25 are respectively connected to the lower surface of the inflator 20 and the surface of the piston rod 22, the third rotating shaft 17 rotates to drive the cam 21 to rotate, the cam 21 rotates to drive the piston rod 22 to reciprocate up and down, and the piston rod 22 reciprocates up and down to drive the piston 23 to reciprocate up and down.

Further, the fixing part comprises a rack plate 27 and an extrusion block 30, the surface of the rotary table 26 is provided with a groove 28 for the rack plate 27 and the extrusion block 30 to extend into, the side surface of the rack plate 27 is fixedly connected with a second spring 29, the end part of the second spring 29 is fixedly connected with the inner wall of the groove 28, the side surface of the extrusion block 30 is provided with a tooth groove fitted with the surface teeth of the rack plate 27, the surface of the extrusion block 30 is provided with a clamping groove 31 for the chalk 3 to extend into, a clamping piece is arranged in the clamping groove 31, the chalk 3 is inserted into the clamping groove 31 when in use and is fixed through the clamping piece arranged in the clamping groove 31, the extrusion block 30 is pressed downwards, and the rack plate 27 teeth and the tooth groove of the extrusion block 30 are matched to drive the rack plate 27 to move, so as to adjust the position of the extrusion block 30, and draw different patterns, the method can be further used for observing the change rule among different graphs, and is convenient for students to understand;

the second spring 29 is a compression spring that is an open coil leaf spring molding mechanism and the most common metal spring structure for resisting axial force generated during compression and the most effective energy storage device in addition to the common cylindrical shape have a variety of shapes including conical cylindrical and hourglass shapes, and the compression spring can have a variety of shapes depending on different applications and design customization can have a variety of shapes;

when the conical compression spring is used, after the load of the conical compression spring is increased to a certain degree, the spring is sequentially tightened from a large ring to a small ring, the characteristic line is changed from linear to gradual increase, the structure is compact, the stability is good, the conical compression spring is mainly used for bearing larger load and reducing vibration, and the occupied space is smaller;

when the butterfly compression spring is used, the butterfly sheets in the butterfly compression spring can obtain different characteristic lines by adopting different combinations, can bear large impact load, has small axial size, and is suitable for occasions requiring strong buffering and vibration reduction capacity and limited axial size.

Furthermore, the driving part comprises a motor 11, the motor 11 is fixedly installed on the surface of the supporting plate 9, the motor realizes closed-loop control of position, speed and torque, the step-out problem of the stepping motor is solved, the high-speed performance is good, the overload resistance is strong, the motor is particularly suitable for occasions with instant load fluctuation and requirements for quick starting, the low-speed running is stable, the stepping running phenomenon similar to the stepping motor cannot be generated in the low-speed running process, the motor is suitable for the occasions with high-speed response requirements, the dynamic corresponding time of acceleration and deceleration of the motor is short, the heating and noise are obviously reduced, the output end of the motor 11 is fixedly connected with the end part of the rotating shaft I10, the rotating shaft I10 is driven to rotate by starting the motor 11 in the use process, the stability of the motor 11 is good, the pattern drawn by the chalk is more accurate, and the teaching quality is improved;

the motor 11 can also be a torque motor, the torque motor has soft mechanical characteristics and can block the rotation, the rotating speed can be automatically reduced when the load torque is increased, and the output torque is increased;

the motor 11 can also be a permanent magnet synchronous motor, which has simple structure, small volume, light weight, low loss and high efficiency, compared with a direct current motor, the permanent magnet synchronous motor has no defects of a commutator, an electric brush and the like of the direct current motor, compared with an asynchronous motor, the permanent magnet synchronous motor does not need reactive exciting current, so the efficiency is high, the power factor is high, the moment inertia ratio is large, the stator current and the stator resistance loss are reduced, and the rotor parameter can be measured and the control performance is good.

In order to improve the practicality of the device, furthermore, the fixed surface of base 1 installs storing box 35, the quantity of storing box 35 is two to with symmetric distribution, when using, mr can put into storing box 35 with the teaching aid, make things convenient for follow-up use, the rational utilization space has improved the practicality of equipment.

In order to facilitate the movement of the device, further, a universal wheel is arranged at the bottom of the base 1, and the base 1 is fixed in position after being moved to a required position through the rolling property and the self-locking property of the universal wheel.

The working principle is as follows: this cycloid demonstration teaching aid that university's mathematics teaching used inserts chalk 3 in draw-in groove 31 when using to it is fixed to it through the clamping piece that sets up in draw-in groove 31.

Then moving the device to attach the chalk 3 to the blackboard, driving the first rotating shaft 10 to rotate by the motor 11, driving the first rotating plate 15 to rotate by the first rotating shaft 10, driving the second rotating plate 16 to rotate and move translationally by the first rotating plate 15, driving the slide block 8 to move translationally by the second rotating plate 16 to rotate and move translationally, driving the third rotating shaft 17 and the rotary table 26 to move translationally by the slide block 8, driving the first gear 12 to rotate by the first rotating shaft 10, driving the second rotating shaft 14 to rotate around the first rotating shaft 10 by the first rotating plate 15, further driving the second gear 13 to rotate around the first gear 12, driving the second gear 13 to rotate by the meshing relationship between the first gear 12 and the second gear 13, driving the second rotating shaft 14 to rotate by the second rotating shaft 14, and driving the third rotating shaft 17 to rotate by the action of the belt transmission mechanism 18, the rotating shaft III 17 rotates to drive the rotating disc 26 to rotate, the rotating disc 26 rotates to drive the chalk 3 to rotate around the rotating shaft III 17, and the chalk 3 moves in a translation mode while rotating around the rotating shaft III 17, so that a pattern is drawn on a blackboard, the drawn pattern is accurate, students can understand the pattern easily, the equipment is simple in structure and convenient to operate, a teacher does not need to draw the pattern manually, time is saved, and teaching efficiency is improved;

the rotating shaft III 17 rotates to drive the cam 21 to rotate, the cam 21 rotates to drive the piston rod 22 to reciprocate up and down, the piston rod 22 reciprocates up and down to drive the piston 23 to reciprocate up and down, and air is blown out from the air outlet pipe 24, so that hard particles or dust on the surface of the blackboard is blown off, and the graphic demonstration effect and the teaching quality are improved;

when the chalk box is used, the extrusion block 30 is pressed downwards, the rack plate 27 is driven to move through the matching between the 27 teeth of the rack plate and the 30 tooth grooves of the extrusion block, so that the position of the extrusion block 30 is adjusted, different patterns can be drawn by the chalk, the chalk box can be used for observing the change rules between the different patterns, and convenience is brought to students to understand.

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims

1. The utility model provides a cycloid demonstration teaching aid that college mathematics teaching used, includes base (1), its characterized in that: the chalk box is characterized by further comprising a bottom plate (4) and a third rotating shaft (17), the base (1) is fixedly connected with the bottom plate (4) through a supporting column (2), side plates (5) are fixedly connected to the two sides of the bottom plate (4), a first connecting plate (6) and a second connecting plate (7) are fixedly connected between the side plates (5) together, a sliding block (8) is connected between the first connecting plate (6) and the second connecting plate (7) in a sliding mode, an opening used for the third rotating shaft (17) to penetrate through and be connected with the third rotating shaft in a fixed-axis rotating mode is formed in the surface of the sliding block (8), a rotating disc (26) is fixedly connected to the end portion of the third rotating shaft (17), chalks (3) are installed on the surface of the rotating disc (26) through fixing parts, a sliding opening (61) used for the fixing rod (19) to penetrate through and be connected with the connecting plate in a sliding mode is formed in the surface of the first connecting plate (6), the tip fixedly connected with inflator (20) of dead lever (19), the side of inflator (20) is provided with intake pipe and outlet duct (24) respectively, sliding connection has piston (23) in inflator (20), the surface of pivot three (17) is provided with and is used for driving piston (23) reciprocating motion's transmission part one, the last fixed surface of bottom plate (4) is connected with backup pad (9), the surface of backup pad (9) is offered and is used for pivot one (10) to pass and with it decide the axle to rotate the mouth of wearing of being connected, be provided with respectively on pivot one (10) and be used for driving slider (8) translation removal's transmission part two with pivot three (17) pivoted transmission part three.

2. The cycloid demonstration teaching aid used in university mathematics teaching of claim 1, wherein: the transmission part II comprises a rotating shaft II (14), the surface fixed connection of the rotating shaft I (10) is provided with a rotating plate I (15), the end part of the rotating plate I (15) is sleeved on the surface of the rotating shaft II (14), the surface dead axle of the rotating shaft II (14) is rotatably connected with a rotating plate II (16), the surface end part of the rotating plate II (16) is provided with a through hole for the rotating shaft III (17) to penetrate and be rotatably connected with the fixed axle, and a driving part for driving the rotating shaft I (10) to rotate is arranged on the supporting plate (9).

3. The cycloid demonstration teaching aid used in university mathematics teaching of claim 2, wherein: the third transmission part comprises a first gear (12), the first gear (12) is fixedly connected to the surface of the first rotating shaft (10), the second gear (13) is fixedly connected to the surface of the second rotating shaft (14), the second gear (13) is meshed with the first gear (12), and the second rotating shaft (14) is in transmission connection with the third rotating shaft (17) through a belt transmission mechanism (18).

4. The cycloid demonstration teaching aid used in university mathematics teaching of claim 1 or 2, wherein: one of the transmission parts comprises a cam (21), the cam (21) is fixedly connected to the surface of the third rotating shaft (17), a piston rod (22) is fixedly connected to the lower surface of the piston (23), the piston rod (22) is abutted to the surface of the cam (21), a first spring (25) is sleeved on the surface of the piston rod (22), and two ends of the first spring (25) are respectively connected with the lower surface of the inflator (20) and the surface of the piston rod (22) in a fixed mode.

5. The cycloid demonstration teaching aid used in college mathematics teaching of claim 4, wherein: the fixing part comprises a rack plate (27) and an extrusion block (30), the surface of the rotary table (26) is provided with a spring II (29), the end part of the spring II (29) is fixedly connected with the inner wall of the groove (28), the side surface of the extrusion block (30) is provided with a tooth groove which is attached to the surface of the rack plate (27), the surface of the extrusion block (30) is provided with a clamping groove (31) which is inserted by the chalk (3), and a clamping piece is arranged in the clamping groove (31).

6. The cycloid demonstration teaching aid used in university mathematics teaching of claim 2, wherein: the driving part comprises a motor (11), the motor (11) is fixedly installed on the surface of the supporting plate (9), and the output end of the motor (11) is fixedly connected with the end part of the first rotating shaft (10).

7. The cycloid demonstration teaching aid used in university mathematics teaching of claim 1, wherein: the upper surface fixed mounting of base (1) has storing box (35), the quantity of storing box (35) is two to with the symmetric distribution, in order to put into the teaching aid in storing box (35), convenient to use, the rational utilization space.

8. The cycloid demonstration teaching aid used in university mathematics teaching of claim 1, wherein: the bottom of base (1) is provided with the universal wheel, through the roll nature and the auto-lock nature of universal wheel to make base (1) remove to required position after, carry out the rigidity.