CN105666468B - A kind of big swing angle planer-type five-axle linkage series-parallel machine tool - Google Patents
A kind of big swing angle planer-type five-axle linkage series-parallel machine tool Download PDFInfo
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- CN105666468B CN105666468B CN201610169598.6A CN201610169598A CN105666468B CN 105666468 B CN105666468 B CN 105666468B CN 201610169598 A CN201610169598 A CN 201610169598A CN 105666468 B CN105666468 B CN 105666468B
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- 238000012545 processing Methods 0.000 claims abstract description 58
- 230000007246 mechanism Effects 0.000 claims abstract description 27
- 238000007792 addition Methods 0.000 claims 1
- 238000005516 engineering process Methods 0.000 abstract description 7
- 238000004519 manufacturing process Methods 0.000 abstract description 7
- 230000009975 flexible effect Effects 0.000 abstract description 4
- 238000010586 diagram Methods 0.000 description 4
- 238000011161 development Methods 0.000 description 3
- 238000007514 turning Methods 0.000 description 3
- 238000013461 design Methods 0.000 description 2
- 238000003754 machining Methods 0.000 description 2
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- 238000012827 research and development Methods 0.000 description 2
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- 239000002184 metal Substances 0.000 description 1
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Classifications
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/003—Programme-controlled manipulators having parallel kinematics
- B25J9/0072—Programme-controlled manipulators having parallel kinematics of the hybrid type, i.e. having different kinematics chains
Abstract
The invention belongs to machinery manufacturing technology fields, more particularly to a kind of big swing angle planer-type five-axle linkage series-parallel machine tool, solve traditional numeric-control machine and existing parallel/hybrid machine tool pivot angle be limited, existing very flexible, rigidity and the drawbacks such as precision is low in terms of elongated class integral structure component is processed.It includes long straight guide, processing module in parallel；Processing module in parallel forms a Spatial Parallel close loop mechanism；Processing module in parallel realizes that moving platform exists by four input drivingsXZThe bidimensional of bidimensional movement and shaft on moving platform in plane in plane rotates, and processing module in parallel existsYDirection of principal axis, which is added with, makes processing module edge in parallelYThe input driving that direction of principal axis slides, makes the moving platform of processing module in parallel realize five-axle linkage campaign.The present invention have simple in structure, working space is big, moving platform flexibility is good, rigidity precision is high,YThe advantages that variation of direction of principal axis driving load is small, dynamic property is good, reconfigurability is strong and the degree of modularity is high.
Description
Technical field
The invention belongs to machinery manufacturing technology fields, and in particular to a kind of big swing angle planer-type five-axle linkage series-parallel machine tool,
It is a kind of achievable elongated precision machined multi-shaft interlocked dress of integral structure component big swing angle that can be applied to digital control processing field
It puts.
Background technology
Parallel institution is the close loop mechanism being made of multiple branches, is had the following advantages compared with traditional serial mechanism：
Parallel machine, using parallel institution as the manufacturing equipment of basic machine, comes across the end of the nineties in last century as a kind of.With parallel connection
Theory of mechanism research deepen continuously and the continuous development of Numeric Control Technology, automatic technology and computer technology, parallel machine by
Gradually become a kind of important new manufacturing equipment and be applied in modern manufacturing industry.Parallel machine compared with conventional serial lathe,
With higher stiffness/weight ratio, faster response speed, higher machining accuracy.So as to be more suitable for high speed, accurate, heavy duty
In the case of processing.And its degree of modularity is high, easily reconstructs, is flexible, so as to be easier to reduce processing cost.It is but in parallel
Lathe there is opposite working space is small, the range of work is limited etc. it is such the shortcomings that, so as to limit its application field.In view of simultaneously
The duality relation in online structure and serial mechanism face in configuration, it is thought that parallel institution and serial mechanism are combined,
So as to propose the configuration of hybrid mechanism, and New-type mixed-coupled lathe is produced using hybrid mechanism as the basic machine of numerically-controlled machine tool.
Series-parallel machine tool integrate simultaneously, the advantage of serial machine tool, while in turn avoid simultaneously, serial configured each the shortcomings that, modern times make
It makes and practicability is had more in industry.Just because of this, in this kind of five-axle linkage series-parallel connection processing based on parallel institution or containing parallel module
The heart gets the attention and studies, and progressively becomes high speed, high-precision, the development trend of high flexibility ratio numerically-controlled machine tool.
In recent years, applied to the fields such as aerospace, railway transportation, defence and military elongated class integral structure component for example：
The global design principle of fuselage, wing, rib, the railway carriage of aircraft etc. increasingly receives attention.Global design it is basic
Concept is, by metal removal from one piece of integral workblank, so as to obtain the superior integral structure component of performance.Its advantages of, is not only
Cycle and the logistics chain of process and assemble are shortened, while also mitigates the weight of structural member.This elongated class integral structure component is big
All part removal rates are high, and it is complex-shaped, porous, wall thickness is thin.Five-axle linkage must be used in order to complete this complicated processing
Numerically-controlled machine tool, and it is more demanding to machine tool capability.Since traditional numeric-control machine is deposited in terms of complicated elongated integral structure component processing
In drawback, new and effective machining tool is found as a urgent task.In view of series-parallel machine tool there is suitable at a high speed,
The advantage of high-precision, heavily loaded processing, Development of Novel series-parallel machine tool will become a kind of effective solution.
It, will simultaneously in " high-grade, digitally controlled machine tools and basic manufacturing equipment " the scientific and technological key special subjects come into effect at the beginning of 2009
Online structure function accessories and 5-axis machining center equipped with such functional component are as one of problem therein.It can
See, parallel module is the key that such equipment research and development.Say that parallel module should possess from the angle of processing flexibility ratio and processing efficiency
Very high rotation flexibility ratio reaches 90 ° for optimal (to realize that vertical sleeping conversion, five faces are processed) with moving platform turning power, and
Where the limitation of this exactly conventional parallel mechanism, the turning power of Sprint Z3 parallel main shaft heads with strongest influence power
Only 40 ° (can not achieve proper five faces processing).As it can be seen that conventional parallel machine is broken through on the premise of high rigidity is ensured
It is the bottleneck sex chromosome mosaicism urgently broken through in the R＆D process of such equipment that structure pivot angle, which is limited,.
The present invention exists for traditional numeric-control machine and existing parallel/hybrid lathe in terms of elongated class integral structure component is processed
The drawbacks of, propose that a kind of long straight guide that is aided with based on modularization four-freedom parallel mechanism realizes the mixed of five-axle linkage processing
Join configuration machine tool.This machine tool applications in elongated class integral structure component processing have it is simple in structure, working space is big, moving platform is flexible
Property good, rigidity precision it is high,YIt is excellent that the variation of direction of principal axis driving load is small, dynamic property is good, reconfigurability is strong and the degree of modularity is high etc.
Point.It can realize and the five-axle linkage of complicated elongated integral structure component is processed.
The content of the invention
The invention belongs to machinery manufacturing technology fields, and in particular to a kind of big swing angle planer-type five-axle linkage series-parallel machine tool,
It solves traditional numeric-control machine and existing parallel/hybrid machine tool pivot angle is limited, is deposited in terms of elongated class integral structure component is processed
Very flexible, rigidity and the drawbacks such as precision is low.
The present invention adopts the following technical scheme that realization：
A kind of big swing angle planer-type five-axle linkage series-parallel machine tool, including：EdgeYThe long straight guide of direction of principal axis setting, parallel connection add
Work module, fixture and workbench；The processing module in parallel includes basic platform, moving platform, cutter and connection basic platform
The first branch, the second branch between moving platform, each several part form a Spatial Parallel close loop mechanism；The processing in parallel
Module realizes that moving platform exists by four input drivingsXZBidimensional movement and moving platform shaft in plane are on it in plane
Bidimensional rotates, and processing module in parallel is mounted on edgeYOn the long straight guide that direction of principal axis is set, andYThere are one make for direction of principal axis addition
Processing module edge in parallelYThe input driving that direction of principal axis slides, makes the moving platform of processing module in parallel realize five-axle linkage campaign.
First branch of the processing module in parallel is (3-RPR)-R type series parallel movement branches, and P represents prismatic pair, R
Revolute pair is represented, the first branch includes plane-parallel type close loop mechanism 3-RPR, and plane-parallel type close loop mechanism 3-RPR includes：Basis
Platform, upper connecting rod I, lower link I, upper connecting rod II, lower link II, upper connecting rod III, lower link III, connecting platform and each movement
Pair, the kinematic pair include：Connect revolute pair R, connection upper connecting rod I and lower link I between basic platform and upper connecting rod I it
Between prismatic pair P, connection lower link I and connecting platform between revolute pair R, connect and turn between basic platform and upper connecting rod II
The revolute pair between prismatic pair P, connection lower link II and connecting platform between dynamic secondary R, connection upper connecting rod II and lower link II
R, connect prismatic pair P between revolute pair R, the connection upper connecting rod III and lower link III between basic platform and upper connecting rod III,
Connect the revolute pair R between lower link III and connecting platform；First branch further includes the rotation between connecting platform and moving platform
Secondary R；The axis of all revolute pair R of plane-parallel type close loop mechanism is mutually parallel and the revolute pair between connecting platform and moving platform
The axis of R is mutually perpendicular to；Wherein connect prismatic pair P, the connection upper connecting rod II and lower link II between upper connecting rod I and lower link I
Between prismatic pair P, connection upper connecting rod III and lower link III between prismatic pair P be input drive motion pair, plane-parallel type
Close loop mechanism realizes that connecting platform existsXZThe bidimensional movement of plane and connecting platform axis edgeYThe one-dimensional rotation of direction of principal axis.
Second branch of the processing module in parallel is RRPS type movement branched chains, and S represents flexural pivot, and the second branch includes：
Upper connecting rod IV, link, lower link IV and each kinematic pair, the kinematic pair include：It connects between basic platform and link
Revolute pair R, connection link and upper connecting rod IV between revolute pair R, connection upper connecting rod IV and lower link IV between movement
Typed ball bearing pair S between secondary P and connection lower link IV and moving platform；Connect the prismatic pair P between upper connecting rod IV and lower link IV
It is input drive motion pair, connects between the revolute pair R between basic platform and link and connection link and upper connecting rod IV
Revolute pair R axis be mutually perpendicular to, two revolute pair R can use Hooke's hinge U to replace.
The axis of the revolute pair R between basic platform and link is connected in second branch with connecting in the first branch
Connect the axis coaxle of the revolute pair R between basic platform and upper connecting rod II.
Described is connected to long straight guide by the prismatic pair P between basic platform and long straight guide by processing module in parallel
On, prismatic pair P is input drive motion pair, realizes processing module in parallelYAxis moves.
In first branch of processing module in parallel, the revolute pair R centers to basis between basic platform and upper connecting rod I
The revolute pair R centers between the distance at revolute pair R centers and basic platform and upper connecting rod III between platform and upper connecting rod II are arrived
The distance at the revolute pair R centers between basic platform and upper connecting rod II is unequal.
Deduced by theory of mechanisms constraint with the relation moved：Moving platform exists compared with basic platform in processing module in parallel
EdgeYDirection of principal axis movement structural constraint thus can not achieve moving platform compared with basic platform edgeYThe movement of axis, moving platform exist
Along the constraint couple parallel to tool axis direction, therefore can not achieve along the rotation parallel to tool axis direction.Moving platform edge
First branch and moving platform be hinged the turning power of shaft up to 115 ° (- 25 °~90 °), edge parallel toYThe rotation energy of direction of principal axis
Power is up to 100 °（-50°~ 50°）, solve the problems, such as that parallel institution pivot angle is limited, processing module in parallel be mounted on edgeYAxis
On the long straight guide in direction, andYDirection of principal axis, which adds one, makes processing module edge in parallelYDirection of principal axis slidably inputs driving, can be with
Realize processing module in parallelYThe a wide range of movement of direction of principal axis solves the problems, such as that conventional parallel mechanism working space is small, so as to fulfill
The a wide range of five-axle linkage campaign of moving platform big swing angle of processing module in parallel.
The present invention combines the advantages of conventional serial lathe and parallel machine, has the simple in structure, working space big, dynamic flat
Platform flexibility is good, rigidity precision is high,YThe variation of direction of principal axis driving load is small, dynamic property is good, reconfigurability is strong and the degree of modularity
The advantages that high.It can realize and the five-axle linkage of complicated elongated integral structure component is processed.
Description of the drawings
Fig. 1 is the general structure schematic diagram of the present invention.
Fig. 2 is the structure diagram of the processing module in parallel in machine tool structure shown in FIG. 1.
Fig. 3 is the structure diagram of the first branch in processing module in parallel shown in Fig. 2.
Fig. 4 is the structure diagram of the second branch in processing module in parallel shown in Fig. 2.
In figure：1st, long straight guide, 2, processing module in parallel, 21, basic platform, 22, moving platform, 23, cutter, 24, first
Branch, 241, upper connecting rod, 242, lower link, 243, upper connecting rod, 244, lower link, 245, upper connecting rod, 246, lower link, 247, connecting platform, the 25, second branch, 251, upper connecting rod, 252, link, 253, lower link, 3, fixture, 4, work
Make platform, 5, example workpiece.
Specific embodiment
The specific embodiment of the present invention is described further with reference to attached drawing.
Such as Fig. 1 ~ Fig. 4, a kind of big swing angle planer-type five-axle linkage series-parallel machine tool includes：EdgeYThe long straight guide 1 of direction of principal axis,
The parts such as processing module 2 in parallel, fixture 3, workbench 4 and example workpiece 5；Processing module 2 in parallel includes basic platform 21, moves and put down
The first branch 24, the second branch 25 between platform 22, cutter 23 and connection basic platform 21 and moving platform 22, each several part form one
A Spatial Parallel close loop mechanism；The processing module in parallel 2 realizes that its moving platform 22 exists by four input drivingsXZPlane
The bidimensional of interior bidimensional movement and shaft on moving platform 22 in plane rotates, and processing module 2 in parallel is mounted on edgeYDirection of principal axis
Long straight guide 1 on, andYDirection of principal axis, which adds one, makes 2 edge of processing module in parallelYDirection of principal axis slidably inputs driving, so that
The moving platform 22 of processing module 2 in parallel can realize five-axle linkage campaign.
As shown in Figure 2,3, the first branch 24 of the processing module in parallel 2 is (3-RPR)-R type series parallel movement branches
（P represents prismatic pair, and R represents revolute pair）, including plane-parallel type close loop mechanism 3-RPR and connecting platform 247 and moving platform
Revolute pair R between 22, this plane-parallel type close loop mechanism can realize that connecting platform 247 existsXZThe bidimensional of plane is mobile and connects
247 axis edge of platformYThe one-dimensional rotation of direction of principal axis；Plane-parallel type close loop mechanism 3-RPR includes：Basic platform 21, upper connecting rod I
241st, lower link I 242, upper connecting rod II 243, lower link II 244, upper connecting rod III 245, lower link III 246, connection are flat
Platform 247 and each kinematic pair, the kinematic pair include：It connects the revolute pair R between basic platform 21 and upper connecting rod I 241, connect
It connects and turns between the prismatic pair P between connecting rod I 241 and lower link I 242, connection lower link I 242 and connecting platform 247
Revolute pair R, connection upper connecting rod II 243 and lower link II between dynamic secondary R, connection basic platform 21 and upper connecting rod II 243
Revolute pair R, connection basic platform 21 between prismatic pair P between 244, connection lower link II 244 and connecting platform 247 with
The prismatic pair P between revolute pair R, connection upper connecting rod III 245 and lower link III 246 between upper connecting rod III 245, connection
Revolute pair R between lower link III 246 and connecting platform 247；The axis of all revolute pair R of plane-parallel type close loop mechanism is mutual
The axis of revolute pair R parallel and between connecting platform 247 and moving platform 22 is mutually perpendicular to；Wherein connect upper connecting rod I 241
Prismatic pair P between lower link I 242, the prismatic pair P being connected between upper connecting rod II 243 and lower link II 244, in connection
Prismatic pair P between connecting rod III 245 and lower link III 246 is input drive motion pair.
As shown in figure 4, the second branch 25 of the parallel connection processing module 2 is UPS type movement branched chains（U represents Hooke's hinge, S
Represent flexural pivot）It can also regard RRPS type movement branched chains as, two of which revolute pair R axis are mutually perpendicular to, this branch 25 includes：
Upper connecting rod IV 251, link 252, lower link IV 253 and each kinematic pair, the kinematic pair include：Connect basic platform 21
Revolute pair R between link 252, the revolute pair R being connected between link 252 and upper connecting rod IV 251, connection upper connecting rod
The typed ball bearing pair S between prismatic pair P, connection lower link IV 253 and moving platform 22 between IV 251 and lower link IV 253；Its
Prismatic pair P between middle connection upper connecting rod IV 251 and lower link IV 253 is input drive motion pair.
As shown in Figure 1, processing module 2 in parallel is connected to by length by the prismatic pair P between basic platform 21 and long straight guide 1
On straight guide 1, prismatic pair P is input drive motion pair, realizes processing module 2 in parallelYAxis moves.
As shown in Fig. 2, in 2 first branch 24 of processing module in parallel, the rotation between basic platform 21 and upper connecting rod I 241
Secondary R centers are to distance and basic platform 21 and the upper connecting rod at the revolute pair R centers between basic platform 21 and upper connecting rod II 243
Revolute pair R centers between III 245 are to the distance not phase at the revolute pair R centers between basic platform 21 and upper connecting rod II 243
Deng this is to overcome a unusual bit-type.The revolute pair between basic platform 21 and link 252 is connected in second branch 25
The axis coaxle of the revolute pair R between basic platform 21 and upper connecting rod II 243 is connected in the axis of R and the first branch 24.
Claims (6)
1. a kind of big swing angle planer-type five-axle linkage series-parallel machine tool, it is characterised in that including：EdgeYThe length that direction of principal axis is set directly is led
Rail, processing module in parallel, fixture and workbench；The processing module in parallel includes basic platform, moving platform, cutter and connection
The first branch, the second branch and connecting platform between basic platform and moving platform, each several part form a Spatial Parallel closed loop
Mechanism, the first branch of the processing module in parallel is (3-RPR)-R type series parallel movement branches, and the first branch includes connection
Revolute pair R between platform and moving platform, the second branch of processing module in parallel is RRPS type movement branched chains；The parallel connection adds
Work module realizes that moving platform exists by four input drivingsXZBidimensional movement and moving platform shaft in plane are on it in plane
Bidimensional rotate, processing module in parallel be mounted on edgeYOn the long straight guide that direction of principal axis is set, andYThere are one direction of principal axis additions
Make processing module edge in parallelYThe input driving that direction of principal axis slides, makes the moving platform of processing module in parallel realize five-axle linkage campaign.
2. big swing angle planer-type five-axle linkage series-parallel machine tool according to claim 1, it is characterised in that：Described first
Chain includes plane-parallel type close loop mechanism 3-RPR, and plane-parallel type close loop mechanism 3-RPR includes：Basic platform, upper connecting rod I, lower company
Bar I, upper connecting rod II, lower link II, upper connecting rod III, lower link III, connecting platform and each kinematic pair, the kinematic pair bag
It includes：It connects the prismatic pair P between the revolute pair R between basic platform and upper connecting rod I, connection upper connecting rod I and lower link I, connect
Revolute pair R between lower link I and connecting platform connects the revolute pair R between basic platform and upper connecting rod II, connects upper connecting rod
Revolute pair R between prismatic pair P between II and lower link II, connection lower link II and connecting platform, connection basic platform with
Prismatic pair P, connection lower link III between revolute pair R between upper connecting rod III, connection upper connecting rod III and lower link III with
Revolute pair R between connecting platform；First branch further includes the revolute pair R between connecting platform and moving platform；Plane-parallel type closes
The axis of all revolute pair R of ring mechanism is mutually parallel and the axis of revolute pair R between connecting platform and moving platform mutually hangs down
Directly；Wherein connect upper connecting rod I and lower link I between prismatic pair P, connection upper connecting rod II and lower link II between prismatic pair P,
Prismatic pair P between connection upper connecting rod III and lower link III is input drive motion pair, and plane-parallel type close loop mechanism 3-RPR is real
Existing connecting platform existsXZThe bidimensional movement of plane and connecting platform axis edgeYThe one-dimensional rotation of direction of principal axis.
3. big swing angle planer-type five-axle linkage series-parallel machine tool as described in claim 1, it is characterised in that：Second branch
Including：Upper connecting rod IV, link, lower link IV and each kinematic pair, the kinematic pair include：Connect basic platform and link
Between revolute pair R, connection link and upper connecting rod IV between revolute pair R, connection upper connecting rod IV and lower link IV between
Typed ball bearing pair S between prismatic pair P and connection lower link IV and moving platform；Connect the movement between upper connecting rod IV and lower link IV
Secondary P is input drive motion pair, connect revolute pair R between basic platform and link and connection link and upper connecting rod IV it
Between revolute pair R axis be mutually perpendicular to, two revolute pair R can use Hooke's hinge U to replace.
4. the big swing angle planer-type five-axle linkage series-parallel machine tool as described in claim 1 or 2 or 3, it is characterised in that：Described
The axis of the revolute pair R between basic platform and link is connected in two branches with being connected basic platform and upper company in the first branch
The axis coaxle of revolute pair R between bar II.
5. big swing angle planer-type five-axle linkage series-parallel machine tool as claimed in claim 4, it is characterised in that：The processing in parallel
Module is connected to by the prismatic pair P between basic platform and long straight guide on long straight guide, and prismatic pair P is input drive motion
Pair realizes processing module in parallelYAxis moves.
6. big swing angle planer-type five-axle linkage series-parallel machine tool as claimed in claim 5, it is characterised in that：The processing in parallel
In the first branch of module, the revolute pair R centers between basic platform and upper connecting rod I turn between basic platform and upper connecting rod II
Dynamic revolute pair R centers between the distance at secondary R centers and basic platform and upper connecting rod III are between basic platform and upper connecting rod II
Revolute pair R centers distance it is unequal.
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| CN201610169598.6A CN105666468B (en) | 2016-03-23 | 2016-03-23 | A kind of big swing angle planer-type five-axle linkage series-parallel machine tool |
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| CN201610169598.6A CN105666468B (en) | 2016-03-23 | 2016-03-23 | A kind of big swing angle planer-type five-axle linkage series-parallel machine tool |
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| CN105666468A CN105666468A (en) | 2016-06-15 |
| CN105666468B true CN105666468B (en) | 2018-05-18 |
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| CN107813331A (en) * | 2016-06-28 | 2018-03-20 | 王祁 | A kind of adjustable underground railway track polishing washing and cleaning operation manipulator |
| CN107825417B (en) * | 2017-09-21 | 2020-05-29 | 燕山大学 | Five-axis series-parallel robot composed of four-degree-of-freedom series-parallel mechanism |
| CN108161490B (en) * | 2017-12-27 | 2019-06-04 | 北京交通大学 | A kind of redundant drive five-freedom parallel machine tool with big corner |
| CN108340353A (en) * | 2018-03-12 | 2018-07-31 | 武汉理工大学 | A kind of imitative wrist joint submissive milling robot in parallel |
| CN112276910B (en) * | 2020-10-29 | 2022-03-18 | 中国民航大学 | Parallel mechanism containing double-sliding-rail composite branched chain |
| CN114310849A (en) * | 2022-01-19 | 2022-04-12 | 燕山大学 | Two-rotation two-movement parallel mechanism |
| CN117444943B (en) * | 2023-12-26 | 2024-03-22 | 济南二机床集团有限公司 | Series-parallel manipulator and manipulator track planning method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US7337691B2 (en) * | 1999-08-05 | 2008-03-04 | Shambhu Nath Roy | Parallel kinematics mechanism with a concentric spherical joint |
| EP1234632A1 (en) * | 2001-02-23 | 2002-08-28 | Willemin Machines S.A. | Kinematic device for programmably supporting and positioning an end element in a machine or an instrument |
| CN1730235A (en) * | 2005-08-29 | 2006-02-08 | 北京航空航天大学 | Redundant parallel mechanism with six degrees of freedom |
| CN100427276C (en) * | 2005-11-11 | 2008-10-22 | 华南理工大学 | Five-freedom parallel robot mechanism with three translational dimensions and two rotational dimensions |
| CN2936617Y (en) * | 2006-07-31 | 2007-08-22 | 华南理工大学 | One-dimension translation, two-dimension rotation three-freedom parallel robot mechanism |
| CN101121265A (en) * | 2007-09-13 | 2008-02-13 | 江苏工业学院 | Single free degree space mechanism for three-dimensional motion |
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