CN110261084A - A kind of bulb ball-and-socket connection kinematic pair interference judging method - Google Patents
A kind of bulb ball-and-socket connection kinematic pair interference judging method Download PDFInfo
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- CN110261084A CN110261084A CN201910552503.2A CN201910552503A CN110261084A CN 110261084 A CN110261084 A CN 110261084A CN 201910552503 A CN201910552503 A CN 201910552503A CN 110261084 A CN110261084 A CN 110261084A
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- 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
- F16C11/06—Ball-joints; Other joints having more than one degree of angular freedom, i.e. universal joints
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/22—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
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- General Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Mechanical Engineering (AREA)
- Length-Measuring Instruments Using Mechanical Means (AREA)
- Length Measuring Devices By Optical Means (AREA)
Abstract
The present invention provides a kind of bulb ball-and-sockets to connect kinematic pair interference judging method, it is characterised in that: defines coordinate system O-UVW as origin using the ball-and-socket center of ball-and-socket part；The symmetry axis for defining ball-end parts is W ' axis；Calculate direction vector of the W axis in earth coordinates O-XYZAnd direction vector of the W ' axis in earth coordinates O-XYZCalculate direction vectorWith direction vectorBetween angleJudging angle can or can not interfere with the size of set angle θ to judge that bulb ball-and-socket connect kinematic pair.This method can judge whether ball-end parts interfere with ball-and-socket part in the design phase, not need to save time and materials cost by drawing three-dimensional machinery model or manufacturing experimently out mechanical template, improve analysis efficiency and accuracy.
Description
Technical field
The present invention relates to bulb pair design fields, dry more specifically to a kind of bulb ball-and-socket connection kinematic pair
Relate to judgment method.
Background technique
It is a kind of typical bulb vice mechanism that bulb ball-and-socket, which connects kinematic pair, and there are three rotary freedoms for tool, is widely applied
In strut class mechanical connection, for example, sports type utility car (SUV) back lifts the support rod of formula tail-gate.
It, generally can be there are two oneself in three rotary freedoms of actual ball motion pair due to the limitation of mechanical structure
By having travel limit on degree direction, so being to have by the relative motion between two mechanical parts of bulb pair connection
Determine stroke range limitation, i.e., constructive interference limits.Therefore before manufacturing and designing the mechanism comprising bulb pair, it is thus necessary to determine that
Bulb pair stroke range is greater than mechanism kinematic range of needs, and bulb-ball-and-socket interference phenomenon otherwise will occur；If two component phases
It is by force more than this limitation to motion range, it will cause mechanical part damages, generate serious security risk.
In checking bulb-ball-and-socket interference method, especially sat in ball-end parts and ball-and-socket part both relative to the earth
When mark system moves, usually there are two types of the examination methods of gathering can be used: first is that being using three-dimensional machinery model views associated mechanisms
It is no to have interference phenomenon；Another kind is whether observation actual machine mechanism has interference phenomenon in operation.Three-dimensional machinery modelling
Advantage be it is intuitive, the disadvantage is that low efficiency, requirement that designer very skillfully grasps Three-dimensional Design Software tool and three-dimensional is set
Meter ability, and need to change three-dimensional repeatedly to select the final scheme not interfered, which results in heavy, unnecessary
Three dimensional design work.Actual machine mechanism observation, it is same as three-dimensional machinery modelling have the advantages that it is intuitive, and to correlation
The technical requirements of personnel are not high, but disadvantage is more obvious: mechanical sample needed for needing reprocessabilty to manufacture experimently, time cost, people
Work cost, material cost consume greatly.
Summary of the invention
To overcome shortcoming and deficiency of the prior art, the purpose of the present invention is to provide a kind of connections of bulb ball-and-socket to move
Secondary interference judging method；This method can judge whether ball-end parts interfere with ball-and-socket part in the design phase, not need to lead to
It crosses and draws three-dimensional machinery model or manufacture experimently out mechanical template, time and materials cost can be saved, improve analysis efficiency and accuracy.
In order to achieve the above object, the technical scheme is that: a kind of connection movement of bulb ball-and-socket
Secondary interference judging method, it is characterised in that: define earth coordinates O-XYZ, defined by origin of the ball-and-socket center of ball-and-socket part
Coordinate system O-UVW, wherein W axis is perpendicular to ball-and-socket part；The symmetry axis for defining ball-end parts is W ' axis；Obtain coordinate system O-UVW
Relative to the mathematics transition matrix of earth coordinates O-XYZ, direction vector of the W axis in earth coordinates O-XYZ is calculated
Obtain mathematics transition matrix of the Z axis of earth coordinates O-XYZ to positive W ' axis, direction of the W ' axis in earth coordinates O-XYZ
VectorAnd then calculate direction vectorWith direction vectorBetween angleJudge that angle and set angle θ's is big
It is small: ifThen determine that bulb ball-and-socket connection kinematic pair will not interfere, otherwise determines that bulb ball-and-socket connects kinematic pair meeting
It interferes.
The principle of the method for the present invention is: in the actual use of bulb pair, ball-end parts pass through non-ball head position and other
Mechanism connection, ball-and-socket part are connect by non-ball-and-socket position with other mechanisms.Due to the limitation of mechanical structure, actual bulb fortune
It moves in three secondary rotary freedoms, the general stroke there are two freedom degree direction will receive limitation.Define coordinate system O-UVW with
Ball-and-socket part is relatively fixed, then ball-end parts, which have, rotates three degree of freedom around the rotation of U axis, around the rotation of V axis, around W axis.
But in two freedom degree directions that U axis and V axis rotate, the stroke of ball-end parts is conditional, therefore bulb pair
There is travel limit.Definition originates in the centre of sphere, is W ' along the symmetry axis of ball-end parts, the ray of the non-ball head position of direction
Axis.When ball-end parts are relative to ball-and-socket part relative motion, the position of W ' axis will be limited in bullet, the cone of bullet
Angle is defined as θ.It bulb-ball-and-socket relative position can be by position of the W ' axis in bullet Lai equivalent description.Therefore, bulb ball
Whether nest connection kinematic pair interferes, and can be judged with whether W ' axis exceeds bullet range；It further says, Ke Yiyong
Direction vector of the W axis in earth coordinates O-XYZWith direction vector of the W ' axis in earth coordinates O-XYZBetween
AngleWhetherRange judges.
Therefore, the method for the present invention can judge whether ball-end parts interfere with ball-and-socket part in the design phase, not need
By drawing three-dimensional machinery model or manufacture experimently out mechanical template, time and materials cost can be saved, improves analysis efficiency and accurate
Degree.
Preferably, direction vector is calculatedMethod be:
Wherein,Mathematics transition matrix for coordinate system O-UVW relative to earth coordinates O-XYZ, is known quantity；
Calculate direction vectorMethod be:
Wherein,For earth coordinates O-XYZ Z axis to the mathematics transition matrix of positive W ' axis, be known quantity；
Calculate direction vectorWith direction vectorBetween angle
One of scheme is: lifting formula switching mechanism for carrying on the back, includes the following steps:
Earth coordinates are defined as O-XYZ using the midpoint of hinge as origin by S1 step, and the folding angle of shutter member is defined
For σ；Obtain the ball-and-socket part ball-and-socket midpoint coordinate (x of the second bulb pair5, y5, z5), and first when folding angle σ=0
The ball-and-socket part ball-and-socket center position coordinates of bulb pair
S2 step, with position coordinatesThe ball-and-socket part ball-and-socket center of the first bulb pair is defined with folding angle σ
Position coordinates are (x3, y3z3)；
S3 step, defines coordinate system O-X ' Y ' Z ' by origin of the ball-and-socket part ball-and-socket midpoint of the second bulb pair, makes coordinate system
The relative position that O-X ' Y ' Z ' and the ball-and-socket part of the second bulb pair are kept fixed, wherein X ' axis passes through the first bulb pair；It will sit
Mark system O-X ' Y ' Z ' is defined as τ around the angle of X ' axis rotation；
S4 step obtains spin matrix T of the coordinate system O-X ' Y ' Z ' relative to earth coordinates O-XYZ3；
S5 step, the ball-and-socket part coordinate system for defining the first bulb pair is O-U3V3W3And second bulb pair ball-and-socket part
Coordinate system is O-U5V5W5；According to telescopic brace rod self structure characteristic dimension, the Z ' axis for obtaining coordinate system O-X ' Y ' Z ' is converted into
With coordinate system O-U3V3W3W3Transition matrix when overlapping of axlesAnd Z ' the axis of coordinate system O-X ' Y ' Z ' is converted into and coordinate
It is O-U5V5W5W5Transition matrix when overlapping of axles
Coordinates computed system O-U3V3W3With coordinate system O-U5V5W5Mathematics relative to earth coordinates O-XYZ angular relationship turns
Change matrixWith
S6 step, the ball-end parts symmetry axis for defining the first bulb pair is W3' axis, the ball-end parts symmetry axis of the second bulb pair
For W5' axis；
S7 step, sets the rotation angle parameter τ of the first bulb pair3、ω3And δ3, Z axis is made to turn τ around X-axis3Angle, then around Y
Axis turns ω3Angle turns δ about the z axis later3Angle, the ball-end parts symmetry axis W with the first bulb pair3' overlapping of axles；Set the second ball
The secondary rotation angle parameter τ of head5、ω5And δ5, Z axis is made to turn τ around X-axis5Then angle turns ω around Y-axis5Angle turns about the z axis later
δ5Angle, the ball-end parts symmetry axis W with the second bulb pair5' overlapping of axles；
Utilize τ3、ω3And δ3, calculate W3' mathematics transition matrix of the axis relative to earth coordinates O-XYZ angular relationship
Utilize τ5、ω5And δ5, calculate W5' mathematics transition matrix of the axis relative to earth coordinates O-XYZ angular relationship
S8 step, calculates relative angle between the ball-and-socket part and ball-end parts of the first bulb pairAnd the second bulb pair
Ball-and-socket part and ball-end parts between relative angle
S9 step, judges angle valueWithSize: ifAndThen determine that bulb ball-and-socket connects
Kinematic pair will not interfere, and otherwise determine that bulb ball-and-socket connection kinematic pair can interfere.
Preferably, in the S2 step, the ball-and-socket part ball-and-socket center position coordinates (x of the first bulb pair3, y3 z3) are as follows:
Wherein, Ry(*) refers to that earth coordinates O-XYZ rotates the mathematics transition matrix at the angle * around Y-axis.
Preferably, the S4 step, spin matrix T of the coordinates computed system O-X ' Y ' Z ' relative to earth coordinates O-XYZ3:
Wherein, Rx(*) refers to that earth coordinates O-XYZ rotates the mathematics transition matrix at the angle * around X-axis；Rz(*) refers to the earth
Coordinate system O-XYZ rotates the mathematics transition matrix at the angle * about the z axis.
Preferably, in the S8 step, angleCalculation method be:
AngleCalculation method be:
Compared with prior art, the invention has the advantages that with the utility model has the advantages that
The method of the present invention can judge whether ball-end parts interfere with ball-and-socket part in the design phase, not need to pass through picture
Three-dimensional machinery model or mechanical template is manufactured experimently out out, time and materials cost can be saved, improve analysis efficiency and accuracy.
Detailed description of the invention
Fig. 1 is the flow chart of the method for the present invention；
Fig. 2 is bulb auxiliary structure schematic diagram；
Fig. 3 is the Definition Principle figure of bulb pair coordinate system O-UVW；
Fig. 4 is the ball-end parts model Definition Principle figure of bulb pair；
Fig. 5 is the model schematic of bulb ball-and-socket range of relative motion；
Fig. 6 is the flow chart of two method of embodiment；
Fig. 7 is that embodiment two carries on the back the structural schematic diagram for lifting formula switching mechanism.
Specific embodiment
The present invention is described in further detail with specific embodiment with reference to the accompanying drawing.
Embodiment one
A kind of bulb ball-and-socket of the present embodiment connects kinematic pair interference judging method, and process is as shown in Figure 1；Definition the earth is sat
Mark system O-XYZ defines coordinate system O-UVW as origin using the ball-and-socket center of ball-and-socket part, and wherein W axis is perpendicular to ball-and-socket part；It is fixed
The symmetry axis of adopted ball-end parts is W ' axis；Mathematics transition matrix of the coordinate system O-UVW relative to earth coordinates O-XYZ is obtained,
Calculate direction vector of the W axis in earth coordinates O-XYZThe Z axis of earth coordinates O-XYZ is obtained to the number of positive W ' axis
Learn transition matrix, direction vector of the W ' axis in earth coordinates O-XYZAnd then calculate direction vectorWith direction to
AmountBetween angleJudge the size of angle Yu set angle θ: ifThen determine that bulb ball-and-socket connects kinematic pair
It will not interfere, otherwise determine that bulb ball-and-socket connection kinematic pair can interfere.
The principle of the method for the present invention is: bulb pair is made of ball-end parts and ball-and-socket part, as shown in Figure 2.Ball-end parts
Bulb position nominal diameter be equal to ball-and-socket part ball-and-socket position nominal diameter.In the actual use of bulb pair, ball
Head part is connect by non-ball head position with other mechanisms, and ball-and-socket part is connect by non-ball-and-socket position with other mechanisms.Due to
The limitation of mechanical structure, in three rotary freedoms of actual ball motion pair, general there are two the strokes of freedom degree direction
It will receive limitation.As shown in figure 3, definition coordinate system O-UVW and ball-and-socket part are relatively fixed, then ball-end parts, which have, surrounds U axis
Rotation rotates three degree of freedom around the rotation of V axis, around W axis.But around two freedom degree sides that U axis and V axis rotate
Upwards, the stroke of ball-end parts is conditional, therefore bulb pair has travel limit.As shown in figure 4, definition originates in ball
The heart, along ball-end parts symmetry axis, to be directed toward the ray of non-ball head position be W ' axis.When ball-end parts are relative to ball-and-socket part phase
When to movement, the position of W ' axis will be limited in bullet as shown in Figure 4, and the cone angle of bullet is defined as θ, vertebral height
For infinity.It bulb-ball-and-socket relative position can be by position of the W ' axis in bullet Lai equivalent description.Therefore, bulb ball
Whether nest connection kinematic pair interferes, and can be judged with whether W ' axis exceeds bullet range；It further says, Ke Yiyong
Direction vector of the W axis in earth coordinates O-XYZWith direction vector of the W ' axis in earth coordinates O-XYZBetween
AngleWhetherRange judges.
Therefore, the method for the present invention can judge whether ball-end parts interfere with ball-and-socket part in the design phase, not need
By drawing three-dimensional machinery model or manufacture experimently out mechanical template, time and materials cost can be saved, improves analysis efficiency and accurate
Degree.
Specifically, the present embodiment includes the following steps:
A1 step, the position coordinates for obtaining ball-end parts and ball-and-socket part, ball-end parts and ball-and-socket part are sat relative to the earth
The position of mark system is also known；
A2 step, setting rotation angle parameter α, β and β make the first rotation alpha angle about the z axis earth coordinates O-XYZ, then around Y-axis
Rotation β angle rotates the angle γ about the z axis later, is overlapped with coordinate system O-UVW；Coordinate system O-UVW is relative to earth coordinates O-XYZ
Mathematics transition matrixIt is known quantity, Z-Y-Z Eulerian angles mode can be used to describe:
Wherein, Rz(*) is the mathematics transition matrix that earth coordinates O-XYZ rotates the angle * about the z axis, Ry(*) is geodetic coordinates
It is the mathematics transition matrix that O-XYZ rotates the angle * around Y-axis；C α=cos (α), s α=sin (α), c β=cos (β), s β=sin
(β), c γ=cos (γ), s γ=sin (γ)；
A3 step calculates direction vector of the W axis in earth coordinates O-XYZ
A4 step obtains the Z axis of earth coordinates O-XYZ to the mathematics transition matrix of positive W ' axisIt is known quantity；Meter
Calculate direction vector of the W ' axis in earth coordinates O-XYZ
A5 step calculates direction vectorWith direction vectorBetween angle
A6 step, the size for judging angle Yu set angle θ: ifThen determine that bulb ball-and-socket connection kinematic pair will not
It interferes, otherwise determines that bulb ball-and-socket connection kinematic pair can interfere.
Embodiment two
The present embodiment bulb ball-and-socket connects kinematic pair interference judging method, lifts formula switching mechanism for carrying on the back；Back lifts formula opening and closing
In mechanism, shutter member 302 can be rotated around hinge 301.304 one end of Telescopic supporting rod passes through the first bulb pair 303 and opens
Closing member 302 connects, and the other end passes through the second bulb pair 305 and the earth (or other mechanisms fixed with 301 relative position of hinge)
Connection.The present embodiment method includes the following steps:
Earth coordinates are defined as O-XYZ using the midpoint of hinge as origin by S1 step, and the folding angle of shutter member is defined
For σ, folding angle σ is known quantity；Obtain the ball-and-socket part ball-and-socket midpoint coordinate (x of the second bulb pair5, y5, z5), and
The ball-and-socket part ball-and-socket center position coordinates of first bulb pair when opening and closing angle σ=0Position coordinates (x5, y5, z5)
It is known quantity；
S2 step, with position coordinatesThe ball-and-socket part ball-and-socket center of the first bulb pair is defined with folding angle σ
Position coordinates are (x3, y3z3):
Wherein, Ry(*) refers to that earth coordinates O-XYZ rotates the mathematics transition matrix at the angle * around Y-axis；
S3 step, defines coordinate system O-X ' Y ' Z ' as origin using the ball-and-socket part ball-and-socket midpoint of the second bulb pair, makes coordinate system
The relative position that O-X ' Y ' Z ' and the ball-and-socket part of the second bulb pair are kept fixed, wherein X ' axis passes through the first bulb pair；It will sit
Mark system O-X ' Y ' Z ' is defined as τ around the angle of X ' axis rotation；
S4 step, spin matrix T of the coordinates computed system O-X ' Y ' Z ' relative to earth coordinates O-XYZ3:
Wherein, Rx(*) refers to that earth coordinates O-XYZ rotates the mathematics transition matrix at the angle * around X-axis；Rz(*) refers to the earth
Coordinate system O-XYZ rotates the mathematics transition matrix at the angle * about the z axis；
S5 step, the ball-and-socket part coordinate system for defining the first bulb pair is O-U3V3W3And second bulb pair ball-and-socket part
Coordinate system is O-U5V5W5；According to telescopic brace rod self structure characteristic dimension, the Z ' axis for obtaining coordinate system O-X ' Y ' Z ' is converted into
With coordinate system O-U3V3W3W3Transition matrix when overlapping of axlesAnd Z ' the axis of coordinate system O-X ' Y ' Z ' is converted into and coordinate
It is O-U5V5W5W5Transition matrix when overlapping of axlesTransition matrixWithIt is known quantity, existing algorithm can be used
It obtains；
Coordinates computed system O-U3V3W3With coordinate system O-U5V5W5Mathematics relative to earth coordinates O-XYZ angular relationship turns
Change matrixWith
S6 step, the ball-end parts symmetry axis for defining the first bulb pair is W3' axis, the ball-end parts symmetry axis of the second bulb pair
For W5' axis；
S7 step, sets the rotation angle parameter τ of the first bulb pair3、ω3And δ3, Z axis is made to turn τ around X-axis3Angle, then around Y
Axis turns ω3Angle turns δ about the z axis later3Angle, the ball-end parts symmetry axis W with the first bulb pair3' overlapping of axles；Set the second ball
The secondary rotation angle parameter τ of head5、ω5And δ5, Z axis is made to turn τ around X-axis5Then angle turns ω around Y-axis5Angle turns about the z axis later
δ5Angle, the ball-end parts symmetry axis W with the second bulb pair5' overlapping of axles；
Utilize τ3、ω3And δ3, calculate W3' mathematics transition matrix of the axis relative to earth coordinates O-XYZ angular relationship
Utilize τ5、ω5And δ5, calculate W5' mathematics transition matrix of the axis relative to earth coordinates O-XYZ angular relationship
S8 step, calculates relative angle between the ball-and-socket part and ball-end parts of the first bulb pairAnd the second bulb pair
Ball-and-socket part and ball-end parts between relative angle
S9 step, judges angle valueWithSize: ifAndThen determine that bulb ball-and-socket connects
Kinematic pair will not interfere, and otherwise determine that bulb ball-and-socket connection kinematic pair can interfere.
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, other any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention,
It should be equivalent substitute mode, be included within the scope of the present invention.
Claims (6)
1. a kind of bulb ball-and-socket connects kinematic pair interference judging method, it is characterised in that: earth coordinates O-XYZ is defined, with ball
The ball-and-socket center of nest part is that origin defines coordinate system O-UVW, and wherein W axis is perpendicular to ball-and-socket part；Define pair of ball-end parts
Axis is referred to as W ' axis；Mathematics transition matrix of the coordinate system O-UVW relative to earth coordinates O-XYZ is obtained, calculates W axis in the earth
Direction vector in coordinate system O-XYZObtain mathematics transition matrix of the Z axis of earth coordinates O-XYZ to positive W ' axis, W ' axis
Direction vector in earth coordinates O-XYZAnd then calculate direction vectorWith direction vectorBetween angleJudge the size of angle Yu set angle θ: ifThen determine that bulb ball-and-socket connection kinematic pair will not interfere, it is no
Then determine that bulb ball-and-socket connection kinematic pair can interfere.
2. bulb ball-and-socket according to claim 1 connects kinematic pair interference judging method, it is characterised in that:
Calculate direction vectorMethod be:
Wherein,Mathematics transition matrix for coordinate system O-UVW relative to earth coordinates O-XYZ；
Calculate direction vectorMethod be:
Wherein,For earth coordinates O-XYZ Z axis to positive W ' axis mathematics transition matrix；
Calculate direction vectorWith direction vectorBetween angle
3. bulb ball-and-socket according to claim 1 connects kinematic pair interference judging method, it is characterised in that: lift formula for carrying on the back
Switching mechanism includes the following steps:
Earth coordinates are defined as O-XYZ using the midpoint of hinge as origin, the folding angle of shutter member are defined as σ by S1 step；
Obtain the ball-and-socket part ball-and-socket midpoint coordinate (x of the second bulb pair5,y5,z5), and the first bulb when folding angle σ=0
Secondary ball-and-socket part ball-and-socket center position coordinates
S2 step, with position coordinatesThe ball-and-socket part ball-and-socket center of the first bulb pair is defined with folding angle σ
Coordinate is (x3,y3z3)；
S3 step, defines coordinate system O-X ' Y ' Z ' by origin of the ball-and-socket part ball-and-socket midpoint of the second bulb pair, makes coordinate system O-X '
The relative position that Y ' Z ' and the ball-and-socket part of the second bulb pair are kept fixed, wherein X ' axis passes through the first bulb pair；By coordinate system
O-X ' Y ' Z ' is defined as τ around the angle of X ' axis rotation；
S4 step obtains spin matrix T of the coordinate system O-X ' Y ' Z ' relative to earth coordinates O-XYZ3；
S5 step, the ball-and-socket part coordinate system for defining the first bulb pair is O-U3V3W3And second bulb pair ball-and-socket part coordinate
System is O-U5V5W5；According to telescopic brace rod self structure characteristic dimension, the Z ' axis for obtaining coordinate system O-X ' Y ' Z ' is converted into and sits
Mark system O-U3V3W3W3Transition matrix when overlapping of axlesAnd Z ' the axis of coordinate system O-X ' Y ' Z ' is converted into and coordinate system
O-U5V5W5W5Transition matrix when overlapping of axles
Coordinates computed system O-U3V3W3With coordinate system O-U5V5W5Mathematics relative to earth coordinates O-XYZ angular relationship converts square
Battle arrayWith
S6 step, the ball-end parts symmetry axis for defining the first bulb pair is W3' axis, the ball-end parts symmetry axis of the second bulb pair is W5’
Axis；
S7 step, sets the rotation angle parameter τ of the first bulb pair3、ω3And δ3, Z axis is made to turn τ around X-axis3Then angle turns around Y-axis
ω3Angle turns δ about the z axis later3Angle, the ball-end parts symmetry axis W with the first bulb pair3' overlapping of axles；Set the second bulb pair
Rotation angle parameter τ5、ω5And δ5, Z axis is made to turn τ around X-axis5Then angle turns ω around Y-axis5Angle turns δ about the z axis later5Angle
Degree, the ball-end parts symmetry axis W with the second bulb pair5' overlapping of axles；
Utilize τ3、ω3And δ3, calculate W3' mathematics transition matrix of the axis relative to earth coordinates O-XYZ angular relationship
Utilize τ5、ω5And δ5, calculate W5' mathematics transition matrix of the axis relative to earth coordinates O-XYZ angular relationship
S8 step, calculates relative angle between the ball-and-socket part and ball-end parts of the first bulb pairAnd second bulb pair ball
Relative angle between nest part and ball-end parts
S9 step, judges angle valueWithSize: ifAndThen determine the connection movement of bulb ball-and-socket
Pair will not interfere, and otherwise determine that bulb ball-and-socket connection kinematic pair can interfere.
4. bulb ball-and-socket according to claim 3 connects kinematic pair interference judging method, it is characterised in that: the S2 step
In, the ball-and-socket part ball-and-socket center position coordinates (x of the first bulb pair3,y3z3) are as follows:
Wherein, Ry(*) refers to that earth coordinates O-XYZ rotates the mathematics transition matrix at the angle * around Y-axis.
5. bulb ball-and-socket according to claim 4 connects kinematic pair interference judging method, it is characterised in that: the S4 step,
Spin matrix T of the coordinates computed system O-X ' Y ' Z ' relative to earth coordinates O-XYZ3:
Wherein, Rx(*) refers to that earth coordinates O-XYZ rotates the mathematics transition matrix at the angle * around X-axis；Rz(*) refers to geodetic coordinates
It is the mathematics transition matrix that O-XYZ rotates the angle * about the z axis.
6. bulb ball-and-socket according to claim 3 connects kinematic pair interference judging method, it is characterised in that: the S8 step
In, angleCalculation method be:
AngleCalculation method be:
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