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WO1998048187A1 - Flexion d'un tube fendu - Google Patents

Flexion d'un tube fendu Download PDF

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Publication number
WO1998048187A1
WO1998048187A1 PCT/US1998/008078 US9808078W WO9848187A1 WO 1998048187 A1 WO1998048187 A1 WO 1998048187A1 US 9808078 W US9808078 W US 9808078W WO 9848187 A1 WO9848187 A1 WO 9848187A1
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WO
WIPO (PCT)
Prior art keywords
tube
split
flexure
link
slit
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
PCT/US1998/008078
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English (en)
Inventor
Michael Goldfarb
John E. Speich
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Vanderbilt University
Original Assignee
Vanderbilt University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Vanderbilt University filed Critical Vanderbilt University
Priority to AU71467/98A priority Critical patent/AU7146798A/en
Priority to US09/403,509 priority patent/US6585445B1/en
Publication of WO1998048187A1 publication Critical patent/WO1998048187A1/fr
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

Links

Classifications

    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
    • F16C11/00—Pivots; Pivotal connections
    • F16C11/04—Pivotal connections
    • F16C11/12—Pivotal connections incorporating flexible connections, e.g. leaf springs

Definitions

  • This invention relates generally to the field of mechanical connections and more particularly to flexure joints.
  • Some classes of machines are particularly sensitive to the presence of backlash and Coulomb friction. Due to the physics of scaling, devices that operate on a microscopic scale are influenced by highly nonlinear surface forces to a much greater degree than those of a conventional scale. Consequently, a scaled-down micromachine is significantly more sensitive to Coulomb friction than its conventional-scale counterpart. Successful development of small-scale and micro-scale precision machines requires elimination or intelligent minimization of surface force behavior.
  • Machines that operate in a zero-gravity environment are also particularly sensitive to Coulomb-type bearing friction, primarily because gravity is no longer the dominate mechanical influence.
  • a flexure- based joint which utilizes deformation as a means of providing movement, is a viable alternative to the conventional revolute joint that does not exhibit any significant backlash or Coulomb friction and is free of lubricants.
  • a diagram of a conventional flexure 2 is shown in Figure 1. The basic characteristics of conventional flexure joints have been studied by several researchers [1,2,3,4]. References
  • a flexure-based structure can approximate the motion of a complex kinematic linkage with negligible stick-slip friction and no backlash. Additionally, the absence of rolling and sliding surfaces produces a device that is free of lubricants and thus extremely conducive to clean environments.
  • Conventional flexures however have several significant deficiencies. One particularly restrictive deficiency is the limited range of motion. Depending on the flexure geometry and material properties, a flexure will begin exhibiting plastic deformation at ranges on the order of five to ten degrees of rotation. In contrast, an ideal revolute joint has an infinite range of motion.
  • the new joint or flexure should: exhibit no backlash or stick-slip behavior; exhibit off-axis stiffnesses significantly greater than a comparable conventional flexure; enable greater range of motion than a comparable conventional flexure; and withstand more load than a conventional flexure.
  • a joint is lacking in the prior art.
  • DISCLOSURE OF THE INVENTION As mentioned previously, an ideal revolute joint is characterized by zero stiffness along the axis of rotation and infinite stiffness along all other axes of loading.
  • Conventional flexure joints offer the benefit of zero backlash and Coulomb friction, but not without limitation.
  • Conventional flexure joints are constrained to a small range of motion and are subject to significant stiffness along the axis of rotation and significant compliance along other axes. This application describes a new flexure that exhibits a considerably larger range of motion and significantly better multi-axis revolute joint characteristics than a conventional flexure.
  • the design of the joint is based upon contrasting the torsional compliance of an open section with its stiffnesses in compression and bending.
  • the torsional mechanics of closed section and open section members are fundamentally and significantly different, while the bending and compressive mechanics of the members are quite similar. This difference in mechanics enables minimization of torsional stiffness and maximization of all other stiffnesses in a nearly decoupled manner.
  • the split-tube flexure includes a thin-walled shaft, a first arm, and a second arm.
  • the shaft is not required to be thin- walled. It may be a generic tube having nearly any conventional of cross-section, including polygonal. Preferably, the tube is a thin-walled nearly closed split cylinder, or hollow shaft. The wall thickness is variable as well. Thus, this invention is not limited to thin-walled hollow shafts. Design requirements, such as a required strength or stiffness, will drive the design parameters (the structural dimensions and material properties).
  • the thin-walled shaft includes a wall, first and second ends, and a length between the first and second ends.
  • the wall defines a lengthwise slit therein.
  • the first link is attached to the shaft.
  • the second link includes a length and is attached to the shaft transversely to the slit.
  • the shaft includes mounting holes at each end to attach the first and second links.
  • the mounting holes should be on a longitudinal axis opposite the slit.
  • split-tube flexure includes a second thin-walled shaft attached to the single split-tube flexure to form a compound split-tube flexure.
  • shafts are aligned co-linear (end-to-end), though the only requirement is that the mounting holes of both tubes remain co-linear.
  • the entire cross section of the first end of the first tube need not be co-linear with the entire cross section of the first end of the second tube, i.e. the respective centroids need not be aligned.
  • a first end of the first tube typically faces a first end of the second tube.
  • the first link is attached to the first ends of the tubes.
  • a second link is attached to second ends of the tube.
  • the links need not be attached at end points of course.
  • the invention includes a method of providing pivotal motion with a flexure joint.
  • the method typically entails providing a first thin-walled shaft (or similar design constrained structure) having a lengthwise slit; attaching a first link to the thin-walled shaft, where the first link extends transversely to the slit (typically perpendicular). And attaching a second link to the first thin- walled shaft, the second link also extending transverse to the slit. Applying a force at the first arm, where the force has a vector component perpendicular to the slit. Applying the axial force will create reactive forces at the second arm, and thereby achieve minimal force resistance along the axis of rotation and relatively large force resistance along other axes of the flexure joint.
  • One objective of the invention is to provide a new flexure- based revolute joint that offers significantly better properties than a conventional flexure. More specific objectives of the invention are to provide a joint which exhibits little to no backlash or stick- slip behavior, and which exhibits off-axis stiffnesses significantly greater than a comparable conventional flexure. A further objective of the invention is to provide a mechanism which enables greater range of motion compared to a conventional flexure.
  • Another objective of the invention is to provide a joint which withstands more load than a conventional flexure.
  • a broader objective of the invention is to provide a joint that enables the implementation of a precision spatially-loaded revolute joint-based machines with well-behaved kinematic characteristics and without the backlash and stick-slip behavior that would otherwise prevent precision control.
  • Another object of the invention is to provide this flexure in a lubricant free environment suitable for 'clean' environments and space-based applications.
  • Figure 1 is a perspective view of a conventional flexure joint, indicating the nominal joint axis of rotation.
  • Figures 2a and 2b are perspective views of closed (left - Fig. 2a) and open (right Fig. 2b) section hollow shafts.
  • Figure 3a, b, and c are perspective views of the split-tube flexure of the present invention in relaxed and flexed positions.
  • Figure 4 is a perspective of view showing the axes of loading for a split-tube flexure joint of the present invention.
  • Figure 5 is a perspective view showing the axes of loading for a conventional flexure joint.
  • Figures 6a and 6b are perspective views showing the geometry of a split-tube flexure joint of the present invention.
  • Figure 7 is a perspective view showing the geometry of a conventional flexure joint.
  • Figure 8a and 8b are perspective (solid model) views of another embodiment of the split-tube flexure of the present invention as used in a two degree-of- freedom five-bar parallel linkage.
  • Figure 9 is a side view of the two dof linkage shown in Figure 8 incorporated into a microbot.
  • Figure 10 is an enlarged side view of the two dof linkage shown in Figure 9.
  • Figure 11 is a pin -joint representation of the two dof linkage shown in Figure 10.
  • Figures 12a and 12b are perspective views illustrating the compound (top) and the simple (bottom) embodiments of the split- tube flexure of the present invention.
  • BEST MODE FOR CARRYING OUT THE INVENTION The mechanics of open versus closed sections
  • Figure 2 shows two hollow shafts, 4 and 6, that are in every manner identical except that one, 6, has a slit along its long axis
  • each shaft having a length L, an outer radius R, and a wall thickness t.
  • R an outer radius
  • t a wall thickness
  • the mechanics of how each bears a torsional load are quite different.
  • the wholly intact shaft reacts mechanically in the same mode as a solid shaft, while the slitted shaft behaves mechanically as a thin flat plate. (Note that in the limit as R approaches infinity, a split cylinder approaches a flat plate.) This dissimilarity in behavior results in very different torsional stiffnesses.
  • torsional stiffness as the ratio of torque about the long axis to the angular deflection about the same, a stress analysis (assuming typical properties such as linearly elastic, homogeneous, isotropic material) illustrates the differences in torsional mechanics.
  • kcs The torsional stiffness of the closed section, kcs, is given by:
  • G is the shear modulus of elasticity
  • L, R, and t are the length, outside radius, and wall thickness of the shaft, respectively.
  • t is the geometry of a thin-walled shaft
  • t typically t less than .15 R
  • the torsional stiffness of the open section is significantly less than of its closed counterpart.
  • Both open and closed section shafts have a bending stiffness given by: ⁇ E ,
  • the axis of rotation is along the top of the tube opposite the split, and not through the center of the tube. Also, the links adjoined by the flexure hinge remain parallel and perpendicular to the axis of rotation though the slit moves with torsion of the cylinder.
  • Figure 6a and 6b show an embodiment of this invention, a single split-tube flexure 10. It shows a thin-walled shaft 20 including a slit 30.
  • the thin-walled shaft 20 generally includes an outer radial dimension R, a wall 25 having thickness t, and a length L. The length L being defined between mounting holes near a first end 21 and a second end 23.
  • the slit 30 is a lengthwise slit typically running the length of the shaft 20.
  • the shaft 20 includes a cylindrical, or tube, shape.
  • Also included in the split-tube flexure 10 is a first link 40 attached to the shaft wall 25, and a second link 50 attached to the shaft wall 25.
  • the first and second links 40 and 50 are attached to the wall at the first and second longitudinally spaced positions along the length of the tube 20.
  • the torsional displacement is linearly related to the longitudinal spacing.
  • the longitudinal spacing should be such that the links are not end to end, or the resultant flexure motion will be from bending of the wall, not torsion. It will be apparent that attaching the links on the wall includes attaching the links on the wall edges. Also the links need not be straight rods or bars as shown in Figures 6a and 6b.
  • the first link 40 and the second link 50 are shown with ends attached to ends of the shaft 20 such that the links 40 and 50 are transverse to, and as shown perpendicular to, the lengthwise slit 30.
  • the links 40 and 50 need not be perpendicular to the slit 30, although, at least one link should be transverse to the slit 30. Transverse being defined as other than parallel.
  • the contact locations will typically be in a line parallel to the slit 30, preferably opposite the slit 30. The contact locations need not be aligned parallel to the slit 30, but the resultant forces, axis of rotation and the mathematics describing the structural dynamics will change.
  • Figure 6b shows the split-tube flexure 10 of Figure 6a further annotated.
  • the thin-walled shaft 20 includes a bottom side 22, a top side 24, a fore side 26, and a back side 28.
  • the first link 40 includes a first portion 42, a second portion 44, and a length 43.
  • the second link 50 includes a first portion 52, a second portion 54, and a length 53.
  • the links 40 and 50 are shown attached to the topside 24 of the shaft 20.
  • the links 40 and 50 though typically attached to the topside 24 of the shaft 20, need not be attached to it.
  • Figure 7 shows a conventional flexure joint 2. It includes a flexure beam width b, a flexure member height h, and a flexure length 1.
  • FIGS. 4 and 5 illustrate split-tube 10 and conventional flexure 2 geometry, respectively, and define the loads (axial loads
  • the objective in the design of a flexure revolute joint is to achieve a minimal stiffness along the axis of rotation and relatively large stiffnesses along all other axes.
  • the inventors refer to the stiffness along the revolute axis as the revolute stiffness, which is defined by k r - ⁇ l ⁇ .
  • Also of primary interest when characterizing joint performance is the allowable range of motion afforded by the joint, a characteristic determined by material yield.
  • a split-tube 10 and a conventional 2 flexure were designed according to desired specifications that were determined by the desired machine performance characteristics.
  • the two joints were designed to have the same revolute stiffness kr, and the joints were required to have the same axial stiffness kai and to withstand a given minimum axial load Fi. Additionally, the two joints were designed of the same stainless steel alloy.
  • Table 2 incorporates the same information as Table 1, but represented instead as the relative characteristics of the split- tube flexure with respect to the conventional flexure.
  • the ratios of k r and kai of the two flexures were set equal by design.
  • all other off-axis stiffnesses of the split- tube flexure 10, kbi, kb2, and ka2 are three to four orders of magnitude larger than the equivalent off-axis stiffnesses of the conventional flexure 2.
  • the split-tube flexure 10 enables 150 degrees of motion, more than five times that of the equivalent conventional flexure 2. This comparison clearly illustrates the improved revolute joint properties offered by the split-tube flexure 10.
  • FIG. 1 Another significant difference between the split-tube 10 and conventional 2 flexure involves the kinematic behavior of the joints.
  • An ideal revolute joint provides a fixed axis of rotation so that the motion of one link with respect to the adjoining link can be characterized as a pure rotation.
  • the illustration of Figure 1 depicts the instantaneous revolute axis associated with a conventional flexure joint. This axis does not remain fixed with respect to either link, but rather translates in the plane as the links rotate.
  • the split-tube flexure 10 has a fixed axis of rotation (opposite and parallel to the split) when the links are attached to the top side of the shaft and are perpendicular to the slit. This enables well-characterized kinematics with a minimal set of measurements.
  • the shaft would typically be a thin- walled cylinder where t « R, however, it is equally apparent that the cross section of the shaft need not be circular.
  • the shaft 20 may include an alternative cross section such as a polygon or other multi-sided cross section.
  • the shaft or tube not be thin-walled.
  • the desired stiffness ratio drives the relationship between t and R.
  • the invention is intended to include other than thin-walled embodiments. A preferred embodiment would, however, typically use a thin-walled cylinder.
  • the reactive forces corresponding to applied loads will, of course, change with various embodiments of the invention.
  • the invention can be used to achieve minimal force resistance along (or about) an axis of rotation, and relatively large force resistance along other axes. Linkages can be used to create minimal resistance along additional axes of rotation.
  • a revolute joint may be formed from a single or double split- tube arrangement.
  • the double split-tube revolute joint also referred to as a compound split-tube (see Figure 12) has been incorporated into a parallel linkage to demonstrate kinematic features of the split-tube flexure.
  • Figures 8a and 8b show perspective view of a two degree-of-freedom (dof) parallel linkage 150 to locate a point 151 within a 2 dof space.
  • Figure 9 shows a side view of the two dof linkage 150 incorporated into a microbot 170.
  • Figure 10 shows an enlarged side view of the linkage 150 shown in Figure 9.
  • a first set of split-tubes 153 connects a first link 152 to a frame 162.
  • a second set of split-tubes 155 connects a second link 154 to the frame 162.
  • the second link 154 being connected to a third link 156 with a third set of split-tubes 157.
  • a fourth link 158 is connected to the third link 156 with a fourth set of split-tubes 159.
  • a fifth set of split-tubes 161 connects the first link 152 to the fourth link 158 between the point 151 and the third link 156 connection 159.
  • Push-pull mechanisms 163 and 164 include a pivot at each end and a cable to attach the pivots to the links and an apparatus to push-pull the push-pull mechanisms.
  • the push-pull mechanisms will also be referred to generally as knife-edge pivots.
  • Knife-edge pivots 163 and 164 are connected to the first link 152 and 154, respectively. Push-pulling the knife-edge pivots 163 and 164 in a vertical plane results in a horizontal and vertical movement of point 151 through the kinematics of the linkage 150.
  • the location of point 151 can be determined as a function of link angles ⁇ 1 and ⁇ 2 .
  • the link angles are related to the vertical distance the knife-edge pivots move through.
  • Figure 11 shows a pin-joint representation of the linkage
  • Link 152 is pin connected at the same location as link 154.
  • the common axis of revolution is achieved by aligning the split- tubes 153 and 155 so that the side opposite the respective slits, i.e. the attachment points, are co-linear.
  • the microbot 170 shown in Figure 9 includes a T-beam support 165 attached to a base 172.
  • An I-beam 173 attached to the base 172 supports support flexures 174.
  • a threaded rod 168 is supported by the support flexures 174 and moved vertically by a voice coil 175.
  • the threaded rod 168 push-pulls the knife-edge pivot 163.
  • a tensioning screw 166 is used to tighten a cable 176 to secure the knife-edge pivot 163 to the second link 154 and a tension block 166. Similar connections are on the other side of the microbot (not shown).
  • Figures 12a and 12b illustrate the compound 60 and simple (or single) 10 joint configurations, both of which are constructed of tubes of equal radius and thickness, and both having the same overall length. Though a compound joint 60 is not limited to use of identical parts.
  • the compound (split-tube) flexure 60 shown in Figure 12a includes a first tube 70 having a wall 72 and having a first end 74 and a second end 76. A length 78 being defined from the first end 74 to the second end 76.
  • the wall 72 also having a lengthwise slit 80.
  • the compound flexure 60 also includes a second tube 110 having a wall 112 and having a first end 114 and a second end 116. A length 118 being defined from the first end 114 to the second end 116.
  • the wall 112 also having a lengthwise slit 119.
  • the second tube 110 is co-linear with the first tube 70 such that the first ends 74 and 114 face each other.
  • a first link 90 is attached to the first tube 70 and the second tube 110 nearer to the first ends 74 and 114 of the tubes than the second ends 76 and 116 of the tubes.
  • a second link 100 is attached to the first tube 70 nearer its second end 76 than its first end 74.
  • the second link 100 is also attached to the second tube nearer its second end 116 than its first end 114.
  • the second link 100 is a bifurcated link having first 122 and second 124 parallel portions attached to the first 70 and second 110 tubes, respectively. And the slits 80 and 119 are co-linear.
  • the first 90 and second 100 links are attached to the first 70 and second 110 tubes at locations lying on a line parallel to the length of the tubes. While this is not required, it is one of the preferred embodiments of the invention because the axis of rotation is constant along the tubes opposite the slit. The axes of rotation of the tubes should be co-linear.
  • a flexure-based revolute joint can be characterized by the ratio of revolute stiffness to axial stiffness and the ratio of revolute stiffness to bending stiffness, both of which in the ideal case would approach zero. Though the absolute value of the revolute stiffness is 4 times larger for the compound joint, the ratio of revolute to axial stiffness and of revolute to bending stiffness are 16 and 4 times smaller, respectively, than the simple joint.

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Mutual Connection Of Rods And Tubes (AREA)

Abstract

Cette invention porte sur un concept de flexion de tube fendu (10 et 60), sur une jonction de révolution de précision unique présentant une plage extrêmement importante de mouvements et de bien meilleures caractéristiques de jonction de révolution multi-axe qu'une flexion traditionnelle (2). Cette flextion de tube fendu (10 et 60) permet la mise en oeuvre de machines de précision à base (170) d'une jonction de révolution chargée spatialement et pourvue de caractéristiques dynamiques et cinématiques à non comportement et sans jeu, et ayant un comportement adhérence-glissement qui serait susceptible autrement d'empêcher la commande des machines de précision.
PCT/US1998/008078 1997-04-21 1998-04-21 Flexion d'un tube fendu Ceased WO1998048187A1 (fr)

Priority Applications (2)

Application Number Priority Date Filing Date Title
AU71467/98A AU7146798A (en) 1997-04-21 1998-04-21 Split tube flexure
US09/403,509 US6585445B1 (en) 1998-04-21 1998-04-21 Split tube flexure

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US4449697P 1997-04-21 1997-04-21
US60/044,496 1997-04-21

Publications (1)

Publication Number Publication Date
WO1998048187A1 true WO1998048187A1 (fr) 1998-10-29

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PCT/US1998/008078 Ceased WO1998048187A1 (fr) 1997-04-21 1998-04-21 Flexion d'un tube fendu

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WO (1) WO1998048187A1 (fr)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109781321A (zh) * 2019-01-29 2019-05-21 西安交通大学 一种裂筒式扭矩传感器

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3700291A (en) * 1971-10-29 1972-10-24 Nasa Two degree inverted flexure
US4261211A (en) * 1976-11-24 1981-04-14 Anschutz & Co. G.M.B.H. Flexure joint, particularly for connecting a gyroscope to its driving shaft
US4269072A (en) * 1979-02-14 1981-05-26 Sperry Corporation Flexure assembly for a dynamically tuned gyroscope
US5213436A (en) * 1990-08-02 1993-05-25 Anschutz & Co. Gmbh Spring joint for pivotally connecting two bodies

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3700291A (en) * 1971-10-29 1972-10-24 Nasa Two degree inverted flexure
US4261211A (en) * 1976-11-24 1981-04-14 Anschutz & Co. G.M.B.H. Flexure joint, particularly for connecting a gyroscope to its driving shaft
US4269072A (en) * 1979-02-14 1981-05-26 Sperry Corporation Flexure assembly for a dynamically tuned gyroscope
US5213436A (en) * 1990-08-02 1993-05-25 Anschutz & Co. Gmbh Spring joint for pivotally connecting two bodies

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109781321A (zh) * 2019-01-29 2019-05-21 西安交通大学 一种裂筒式扭矩传感器
CN109781321B (zh) * 2019-01-29 2021-03-23 西安交通大学 一种裂筒式扭矩传感器

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