CN107813342A - A kind of wire saws parallel robot Trinity structural stability evaluation method - Google Patents
A kind of wire saws parallel robot Trinity structural stability evaluation method Download PDFInfo
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- CN107813342A CN107813342A CN201711047293.9A CN201711047293A CN107813342A CN 107813342 A CN107813342 A CN 107813342A CN 201711047293 A CN201711047293 A CN 201711047293A CN 107813342 A CN107813342 A CN 107813342A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators
- B25J19/0095—Means or methods for testing manipulators
Abstract
The invention discloses a kind of wire saws parallel robot Trinity structural stability evaluation method, on the basis of the solution of rope redundancy pulling force, propose that two position performance factors and two rope pulling force characteristic factors describe end effector and influences of the Suo Lali to its stability on most weak direction constrained when the location of working space and end are in the position respectively;Influence of the end effector posture to its structural stability is evaluated by posture influence function f (φ, θ, ψ);On the basis of being determined in position and rope pull performance factor and posture influence function, pass through formula Ωm(x, y, z, φ, θ, ψ)=Ωn(x, y, z) f (φ, θ, ψ) establishes wire saws parallel robot Trinity structural stability evaluation index and evaluation method.The present invention has filled up the deficiency of current wire saws parallel robot estimation of stability index and evaluation method, and Research foundation is established to lift its stability.
Description
Technical field
The present invention relates to wire saws parallel robot stability study field, and in particular to a kind of wire saws parallel robot
Trinity structural stability evaluation method.
Background technology
Wire saws parallel robot using the rope with flexible characteristic due to that, as driving element, can be reached larger
Speed and acceleration, however, the structural stability of its end effector, which turns into, limits its major obstacle further developed.
Svinin et al. are analyzed the stability of Complete Bind rigidity parallel robot using stiffness matrix.Its research shows,
When stiffness matrix produced by flexibility of joint coefficient be on the occasion of when, Complete Bind parallel robot is stable.But due to interior
Stiffness matrix caused by power is unsymmetrical matrix, so when there is external interference power to act on end effector, completely about
The motion of beam parallel robot is likely to be unstable.Although its method can be by stiffness matrix to the steady of parallel robot
Qualitative to be evaluated, still, it studies the parallel robot for being only limitted to rigid rod driving, also, is reflected using stiffness matrix
The stability of parallel robot end movement, only it is merely that stability is illustrated in terms of constraint, it is impossible to from restraining force
More comprehensively reflect the stability of end motion with the aspect of current end present position two.
Behzadipour et al. propose a kind of method of new solution global stiffness matrix, and utilize solved it is total just
Degree matrix goes to evaluate the stability of wire saws parallel robot.But it solves the method for global stiffness matrix and is built upon rope
Rope is reduced on the basis of Hookean spring, larger with the rope model error of reality, and its stiffness matrix solved exists certain
Error.Also, solution of the above-mentioned document to stability is excessively harsh, the state of its stability only exists stabilization and unstable two
Kind state, it is impossible to stability that is objective, quantitatively reflecting wire saws parallel robot end movement.Bosscher et al. are ground
The balancing method of stability of the underconstrained wire saws parallel robot based on slope is studied carefully.Although this method can quantitatively reflect
The stability of wire saws parallel robot end movement, still, influences of the Suo Lali to stability is not accounted for, not to complete yet
The wire saws parallel robot of staff cultivation and redundant constaint is studied.Marco et al. propose a kind of constrained optimization method
The stability of model of the underconstrained wire saws parallel robot based on geometry static balancing is analyzed.But this method pair
The research of stability is only limitted to the underconstrained wire saws parallel robot in static balancing.Mohammad et al. are led to rope
The Dynamic Modeling and control for drawing parallel robot are studied.A kind of control algolithm based on rope length is proposed, and to calculating
The stability of method is studied.But its research be in itself control algolithm stability, without be related to end perform
The stability of device motion.Liu et al. propose three minimum rope pulling force characteristic factors, to wire saws parallel robot most
Distribution situation of the little Suo pulling force in working space has carried out systematic research, and by minimum Suo Lali and its end effector
Relation between structural stability is qualitatively analyzed.But the document does not establish end effector mathematically
Quantitative relationship between structural stability and minimum Suo Lali.Liu et al. are right in terms of the Suo Lali two of position and constraint
The structural stability of wire saws parallel robot is analyzed, and use weighting mathematical method establish end effector for
The location point and Suo Lali that the structural stability of the wire saws parallel robot of point mass is presently in end effector it
Between mathematical relationship, referred to as stability.The index can use the numeral in [0,1] section to reflect end effector for point matter
The structural stability of the wire saws parallel robot of amount.But the document does not account for end effector posture to wire saws simultaneously
Join the influence of robot structural stability.
Wire saws parallel robot using the less flexible rope of rigidity be used as driving element, cause make it have poor rigidity,
The weakness such as end effector stability difference, turning into restriction, it obtains a wide variety of bottleneck.Its structural stability both depended on
In structure parameters, the configuration of redundant drive power, while the control algolithm depending on used by are also depended on, three is inseparable,
Influence each other.And current present situation is, the structural stability of wire saws parallel robot end effector is presently in end
Relationship is left to be desired between the Suo Lali that pose, rope constrain.
The content of the invention
To solve the above problems, the invention provides a kind of evaluation of wire saws parallel robot Trinity structural stability
Method, the deficiency of current wire saws parallel robot estimation of stability index and evaluation method is filled up, it is stable to lift it
Performance establishes Research foundation.
To achieve the above object, the technical scheme taken of the present invention is:
A kind of wire saws parallel robot Trinity structural stability evaluation method, comprises the following steps:
S1, on the basis of the solution of rope redundancy pulling force, propose two position performance factors and two Suo Lali respectively
Can the factor describe end effector and be presently in position and Suo Lali pairs on most weak direction is constrained when end be in the position
The influence of end effector stability, specifically comprises the following steps:
S11, propose two position performance factorsWithEnd effector present position point is weighed away from the location point institute
The distance of the heart and coboundary in a horizontal plane, is expressed as:
In formula, P is that end effector is presently in location point;XPFor the coordinate vector at the point P of current location;Wire saws are simultaneously
Connection robot working space's vertical center line is represented with a;Q be end effector be presently in horizontal plane where location point P with it is vertical
Center line a intersection point;M is vertical center line a and the upper top surface of robot working space intersection point;γP,γQAnd γMRespectively end is held
Row device is in the angle of the direction of Suo Lali minimum ropes and horizontal plane at location point P, Q and M;
S12, rope redundancy pulling force determination on the basis of, propose two rope pulling force characteristic factorsWithDescription is minimum
Distributions of the Suo Lali on working space horizontal section and vertical center line, is expressed as:
In formula, XPThe coordinate vector at location point P is presently in for end effector;TP,min,TQ,minAnd TM,minRespectively
The minimum Suo Li that end effector is at location point P, Q and M.
S2, influence of the posture of end effector to its structural stability is evaluated by posture influence function f (φ, θ, ψ);
Wherein, when (φ, θ, ψ) represents that end effector of robot is in current location point respectively, around its local coordinate system
O '-x '-y '-z ' attitude angle;When end effector of robot is in a certain defined location point of working space, its three appearances
State angle (φ=0, θ=0, ψ=0) (as illustrated, the attitude angle of end effector of robot is all 0), referred to as normotopia, relatively
It is preferable in remaining posture, end effector of robot stability;If in three attitude angles, at least one attitude angle is not 0, is claimed
Be loxosis, end effector of robot structural stability is poor;Attitude angle is bigger, and structural stability is poorer;It is not 0 posture
Angle is more, and structural stability is also poorer.By analysis we can see that:Attitude angle at the point of end effector present position
For (0,0,0) when, wire saws parallel robot end effector structures stability is best;Conversely, work as position residing for end effector
An attitude angle at putting is maximum angular (φmax,θmax,ψmax) when, its structural stability is worst.
S3, on the basis of above-mentioned position and rope pull performance factor and posture influence function determine, by following
Formula defines the Trinitarian structural stability evaluation index of wire saws parallel robot:
Ωm(x, y, z, φ, θ, ψ)=Ωn(x,y,z)f(φ,θ,ψ)
Wherein, Ωm∈ [0,1], its numerical value are referred to as stability,Represent
End for point mass wire saws parallel robot structural stability, Ωn∈ [0,1], p1,p2,q1And q2It is to be more than less than 1
0 constant, and p1+p2=1, q1+q2=1.
Preferably, the posture influence function must possess following property:
1) in order to reflect the Stability Analysis of Structures degree of wire saws parallel robot using the numerical value in [0,1] section,
The codomain of posture influence function must be in [0,1] section;
2) when end effector is at a certain defined location point of working space, the Stability Analysis of Structures of wire saws parallel robot
Property weakens with the increase of attitude angle.
3) following two extreme cases need to be considered:
(1) attitude angle of end effector present position point is (0,0,0), the structural stability of wire saws parallel robot
It is most strong;
(2) attitude angle of end effector present position point is (φmax,θmax,ψmax), the knot of wire saws parallel robot
Structure stability is most weak;Wherein, attitude angle (φmax,θmax,ψmax) it is the maximum critical appearance that end effector of robot can be stablized
State angle;When end effector is in a certain defined location point of working space, any attitude angle is more than maximum in three attitude angles
Critical attitude angle, end effector can not reach stable.
The invention has the advantages that:
The present invention performs from end effector in the location of working space, posture and in current pose Dian Chu ends
Three aspects such as minimum Suo Lali that device is subject to are studied its structural stability, propose wire saws parallel robot three one
Body structural stability evaluation method, for weighing stabilization of the wire saws parallel robot end effector in whole working space
Property.The deficiency of current wire saws parallel robot estimation of stability index and evaluation method is filled up, to lift its stability
Research foundation can be established, promotes there can be a comprehensive complete quantitative measurement to wire saws parallel robot stability, for rope
The estimation of stability of traction parallel robot establishes solid foundation.
Brief description of the drawings
Fig. 1 is position and rope pulling force characteristic factor schematic diagram in the embodiment of the present invention
Embodiment
In order that objects and advantages of the present invention are more clearly understood, the present invention is carried out with reference to embodiments further
Describe in detail.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to limit this hair
It is bright.
Because wire saws parallel robot using the rope of light soft drives end effector, so when it is by outer
When boundary disturbs, it is possible to change the current pose in its end under the forcing of external interference.If external interference changes
The pose of wire saws parallel robot end, then robot is unstable.So the stability of wire saws parallel robot is
Refer to:When robot is by external interference, it constrains the ability that external interference is resisted on most weak direction.Wire saws parallel robot
Structural stability mainly by three aspect influenceed:End effector is in the location of working space, posture and works as
There is the Suo Lali that pulling force minimum rope is subject in rope in front position point place.For the certain all pose points of minimum Suo Lali,
Because its residing pose in working space is different, the stability of end may be different;And in identical pose point, due to end
The difference of load suffered by actuator is held, the redundancy rope pulling force of solution is different, in turn results in the minimum Suo Lali of same pose point
Difference, the stability of its end are also different.
Due to wire saws parallel robot resist the outer structural stability can for carrying interference both with the pose residing for end's platform
It is relevant, it is also related to the size of rope tensility.The present invention is presently in position, terminal angle and minimum about from end effector
Three aspects such as Suo Lali of beam are analyzed the stability of wire saws parallel robot, and mathematically establishing can be accurately anti-
The Trinity structural stability evaluation index reflected between above-mentioned three and system architecture stability.Performance factor, rope in position
On the basis of power performance factor and posture influence function, the stability that three moves to end effector is integrated, entered
And more objectively reflect the structural stability of end effector comprehensively.The structural stability index is used between section [0,1]
Numerical value weigh the structural stability of wire saws parallel robot, and then can be used for trying to achieve the wire saws to meet certain requirements
Parallel robot steady operation space.Therefore, the present invention proposes a kind of wire saws parallel robot Trinity Stability Analysis of Structures
Property evaluation method, comprises the following steps:
S1, rope redundancy pulling force solution on the basis of, referring specifically to document
Gosselin C,Grenier M.On the determination of the force distribution
in overconstrained cable-driven parallel mechanisms[J].Meccanica,2011,46(1):
3-15. or Liu P, Qiu Y, Su Y, et al.On the minimum cable tensions for the cable-
Based parallel robots [J] .Journal of Applied Mathematics, 2014,2014. or Liu Peng flexible cables
Parallel robot mechanical analysis and estimation of stability [D] Xian Electronics Science and Technology University are drawn, 2015. propose two positions respectively
Performance factor and two rope pulling force characteristic factors describe the rope that end effector is presently on position and the most weak direction of constraint
Influence of the pulling force to end effector stability;Specifically comprise the following steps:
S11, propose two position performance factorsWithWeigh end effector and be presently in location point away from the position
The distance of horizontal plane center and coboundary where point, is expressed as:
In formula, as shown in figure 1, P, which is end effector, is presently in location point;XPFor the coordinate at the point P of current location to
Amount;Wire saws parallel robot working space vertical center line is represented with a;Q is that end effector is presently in water where location point P
Plane and vertical center line a intersection point;M is vertical center line a and the upper top surface of robot working space intersection point;γP,γQAnd γMPoint
Not Wei end effector be in the angle of the direction of Suo Lali minimum ropes and horizontal plane at location point P, Q and M;
S12, rope redundancy pulling force determination on the basis of, propose two rope pulling force characteristic factorsWithDescription is minimum
Distributions of the Suo Lali on the horizontal section of working space and vertical center line, is expressed as:
In formula, XPThe coordinate vector at location point P is presently in for end effector;TP,min,TQ,minAnd TM,minRespectively
The minimum Suo Li that end effector is at location point P, Q and M.
S2, influence of the terminal angle to its structural stability is evaluated by posture influence function f (φ, θ, ψ);
Wherein, when (φ, θ, ψ) represents that end effector of robot is in current location point respectively, around its local coordinate system
O '-x '-y '-z ' attitude angle;When end effector is in a certain defined location point of working space, its three attitude angles
(φ=0, θ=0, ψ=0) (as shown in figure 1, the attitude angle of end effector of robot is all 0), referred to as normotopia, relative to
Remaining posture, end effector of robot stability are preferable;If in three attitude angles, at least one attitude angle is not 0, is referred to as
It is poor for loxosis, end effector of robot structural stability;Attitude angle is bigger, and structural stability is poorer;It is not 0 attitude angle
More, structural stability is also poorer;By analysis we can see that:When the attitude angle of end effector present position point is
When (0,0,0), structural stability of the wire saws parallel robot end effector at the point of current location is best;Conversely, when end
The attitude angle for holding actuator present position point is maximum angular (φmax,θmax,ψmax) when, its structural stability is worst.
S3, on the basis of above-mentioned position and rope pull performance factor and posture influence function determine, by following
Formula defines wire saws parallel robot Trinity structural stability evaluation index:
Ωm(x, y, z, φ, θ, ψ)=Ωn(x,y,z)f(φ,θ,ψ) (5)
Wherein, Ωm∈ [0,1], its numerical value are referred to as stability,Represent
End for point mass wire saws parallel robot structural stability, Ωn∈ [0,1], p1,p2,q1And q2It is to be more than less than 1
0 constant, and p1+p2=1, q1+q2=1.
The posture influence function must possess following property:
1) in order to reflect the Stability Analysis of Structures degree of wire saws parallel robot using the numeral in [0,1] section,
The codomain of posture influence function must be in [0,1] section;
2) a certain defined location point of working space, the Stability Analysis of Structures of wire saws parallel robot are in end effector
Property reduces with the increase of attitude angle.
3) following two extreme cases need to be considered:
(1) attitude angle that end effector is presently in location point is (0,0,0), and the structure of wire saws parallel robot is steady
It is qualitative most strong;
(2) attitude angle that end effector is presently in location point is (φmax,θmax,ψmax), wire saws parallel robot
Structural stability is most weak;Wherein, attitude angle (φmax,θmax,ψmax) for end effector of robot can stablize it is maximum critical
Attitude angle;When end effector of robot, any attitude angle is big in a certain defined location point of working space, three attitude angles
In maximum critical attitude angle, end effector can not reach stable.
Described above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should
It is considered as protection scope of the present invention.
Claims (4)
- A kind of 1. wire saws parallel robot Trinity structural stability evaluation method, it is characterised in thatS1, on the basis of the solution of rope redundancy pulling force, propose respectively two position performance factors and two rope pulling force characteristics because Son description end effector constrains the Suo La on most weak direction when the location of working space and end are in the position Influence of the power to its stability;S2, influence of the posture of end effector to its structural stability is evaluated by posture influence function f (φ, θ, ψ), its In, when (φ, θ, ψ) represents that end effector of robot is in current location point respectively, around its local coordinate system o '-x '-y '-z ' Attitude angle;S3, on the basis of being determined in above-mentioned position and rope pull performance factor and posture influence function, pass through below equation Define wire saws parallel robot Trinity structural stability evaluation index:Ωm(x, y, z, φ, θ, ψ)=Ωn(x,y,z)f(φ,θ,ψ)Wherein, Ωm∈ [0,1], its numerical value are referred to as stability,For point mass The structural stability of wire saws parallel robot, Ωn∈ [0,1], p1,p2,q1And q2It is to be less than 1 constant for being more than 0, and p1+ p2=1, q1+q2=1.
- 2. a kind of wire saws parallel robot Trinity structural stability evaluation method as claimed in claim 1, its feature It is, the step S1 specifically comprises the following steps:S11, propose two position performance factorsWithCurrent location point residing for end effector is weighed away from where the location point Horizontal plane center and the distance of coboundary, are expressed as:In formula, P is that end effector of robot is presently in location point;XPFor the coordinate vector at the point P of current location;Wire saws Parallel robot working space vertical center line is represented with a;Q is horizontal plane where end effector is presently in location point P with erecting Straight center line a intersection point;M is vertical center line a and the upper top surface of robot working space intersection point;γP,γQAnd γMRespectively end Actuator is in the angle of the direction of Suo Lali minimum ropes and horizontal plane at location point P, Q and M;S12, rope redundancy pulling force determination on the basis of, propose two rope pulling force characteristic factorsWithMinimum rope is described to draw Distribution of the power on working space horizontal section and vertical center line, is expressed as:In formula, XPThe coordinate vector at location point P is presently in for end effector;TP,min,TQ,minAnd TM,minRespectively end The minimum Suo Li that actuator is at location point P, Q and M.
- 3. a kind of wire saws parallel robot Trinity structural stability evaluation method as claimed in claim 1, its feature It is, when the attitude angle of end effector present position point is (0,0,0), structure of the end effector at the point of current location Stability is best;Conversely, when the attitude angle of end effector present position point is maximum angular (φmax,θmax,ψmax) when, its structure Stability is worst.
- 4. a kind of wire saws parallel robot Trinity structural stability evaluation method as claimed in claim 1, its feature It is, the posture influence function f (φ, θ, ψ) must possess following property:1) codomain of posture influence function must be in [0,1] section;2) when end effector of robot is in, working space is a certain to be determined at location point, and the structure of wire saws parallel robot is steady It is qualitative to weaken with the increase of attitude angle;3) following two extreme cases need to be considered:(1) attitude angle of current location point residing for end effector is (0,0,0), the structural stability of wire saws parallel robot Most strong, referred to as normotopia, i.e. end effector attitude angle are equal to point mass to robot architecture's stability without influence, its numerical value The structural stability of wire saws parallel robot;(2) attitude angle of current location point residing for end effector is (φmax,θmax,ψmax), the knot of wire saws parallel robot Structure stability is most weak;Wherein, attitude angle (φmax,θmax,ψmax) it is the maximum critical appearance that end effector of robot can be stablized State angle;When end effector is in, working space is a certain to be determined at location point, and any attitude angle is more than maximum in three attitude angles Critical attitude angle, end effector can not reach stable.
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CN110861081A (en) * | 2019-10-14 | 2020-03-06 | 北京航空航天大学 | Autonomous positioning method for under-constrained cable parallel robot end effector |
CN110948481A (en) * | 2019-11-05 | 2020-04-03 | 佛山科学技术学院 | Stability evaluation method of rope-traction parallel robot based on pose cable force stiffness |
CN110948481B (en) * | 2019-11-05 | 2022-12-06 | 佛山科学技术学院 | Stability evaluation method of rope-traction parallel robot based on pose cable force stiffness |
CN110948485A (en) * | 2019-11-21 | 2020-04-03 | 佛山科学技术学院 | Calculation method for accurate numerical solution of rope traction parallel robot flexible cable catenary model |
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CN112632768A (en) * | 2020-12-21 | 2021-04-09 | 厦门大学 | Stability analysis method for under-constrained rope traction parallel mechanism |
CN112632768B (en) * | 2020-12-21 | 2022-05-03 | 厦门大学 | Stability analysis method for under-constrained rope traction parallel mechanism |
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