CN105653820B - A kind of Delta robot architecture's Parameters design for overcoming universal joint corner to limit - Google Patents
A kind of Delta robot architecture's Parameters design for overcoming universal joint corner to limit Download PDFInfo
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- CN105653820B CN105653820B CN201610052523.XA CN201610052523A CN105653820B CN 105653820 B CN105653820 B CN 105653820B CN 201610052523 A CN201610052523 A CN 201610052523A CN 105653820 B CN105653820 B CN 105653820B
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Abstract
The invention discloses a kind of Delta robot architecture's Parameters designs for overcoming universal joint corner to limit, and belong to Delta robot architecture's parameter designing field.The angle range of universal joint is usually one 90 ° of cone angle space, has a certain distance compared to the angle range of spherical hinge, therefore in order to allow the Delta robot for using universal joint to have preferable working space, need to optimize its structure by calculating.The present invention can overcome influence of the universal joint to Delta robot working space, can possess bigger working space.Calculating process of the invention the following steps are included: clear Delta robot known parameters and parameter to be designed；Establish rectangular coordinate system；Four kinds of peculair motion poses of master arm and slave arm are determined in coordinate system；It can be to the Delta robot architecture's parameter for overcoming universal joint corner to limit according to desired workplace design.
Description
Technical field
The present invention relates to a kind of method for designing Delta robot architecture parameter, which is made using universal joint
Articulation piece between master arm and slave arm and between slave arm and moving platform.
Background technique
With the continuous propulsion of Chinese Industrialization process, industrial robot application technology has obtained quick development.Industry
Critical function component of the robot as equipment manufacture, plays more and more important in job-shop automation logistics production system
Effect.Delta robot is one of most successful parallel robot of current business application, with speed is fast, precision is high, structure
Simply, the advantages that load capacity is big, easy to control has a wide range of applications in production fields such as food, drug, medical treatment.
The shoulder joint of Delta robot hingedly generallys use that spherical hinge is hinged, is different from traditional spherical hinge, this flexural pivot
Chain uses separate structure, and ball-and-socket part and ball pin part contact surface are not more than hemisphere face.Such structure design is so that ball pin
Deflection angle can be close to ± 90 °, compared to traditional spherical hinge, angle range is greatly promoted.But it uses this hinged
Mode haves the defects that very big, i.e., with the increase of slave arm pivot angle, the weight bearing ability and dynamic performance of robot will be big
Width decline.If there is still a need for the load capacity for improving robot in this case, the stiffness system of increase spring can only be passed through
Number increases ball-and-socket and ball pin contact force, but such that frictional force also increases with it, will increase the internal loss of system.
Replacing spherical hinge to carry out shoulder joint using universal joint hingedly can be very good to solve the above problems, and be current compare
Ideal solution.Firstly, universal joint itself is connected as an entirety, it is not required to external force and moves it constrain；Secondly, ten thousand
The intensity of part itself is limited to section bearing capacity, rather than the spring tension in the design of above-mentioned spherical hinge；Finally, universal joint is adopted
With bearing arrangement, compared to the internal loss that the face contact of spherical hinge can reduce frictional force generation.But use the Delta of universal joint
The working space of robot will receive the limitation of universal joint working space, be one 90 ° since the angle range of universal joint is smaller
Cone angle space so that the motion range of Delta robot is limited, working space is also opposite to become smaller.Therefore, in order to overcome
The smaller influence to the Delta robot using universal joint of universal joint angle range, makes it have a more satisfactory job
Space needs the structural parameters to Delta robot to optimize.
Summary of the invention
The technical problem to be solved in the present invention is that for using universal joint as between master arm and slave arm and from
The Delta robot of articulation piece between swing arm and moving platform, the working space of the robot is due to universal joint angle range is smaller
It is limited, propose a kind of Delta robot architecture's Parameters design for overcoming universal joint corner to limit, this method can basis
The predetermined parameter designing of expectation working space parameter and part of Delta robot goes out the active brachium of Delta robot
Degree, the mounted angle of driven arm lengths, universal joint on moving platform, while slave arm maximum pendulum angle and moving platform can also be found out
Z-axis coordinate minimum value of the center under basis coordinates system.Structural parameters by this method to the Delta robot for using universal joint
It optimizes, the Delta robot designed is enable to overcome the smaller limit to Delta robot working space of universal joint corner
System, so that the working space of Delta robot can satisfy desired working space.
The technical scheme of the present invention is realized as follows:
The following steps are included:
Step 1: explicitly known according to the predetermined parameter of the expectation working space parameter of Delta robot and part
Parameter and parameter to be designed, it is known that parameter includes:
ρorder: it is expected the radius of working space；
H: it is expected the height of working space；
re: the equivalent hinge joint of master arm is away from fixed platform centre distance；
δ: the shortest distance of two-arm hinge joint to y-axis；
αmin: slave arm minimum angle-of-incidence；
βmax: slave arm radial angle maximum value；
Structural parameters to be designed include:
L: driven arm lengths；
L: active arm lengths；
αm: mounted angle of the universal joint on moving platform；
z0: z-axis coordinate minimum value of the moving platform center under basis coordinates system；
γmax: slave arm maximum pendulum angle；
Step 2: rectangular coordinate system is established: using wherein one group of master arm and slave arm as object, in slave arm without swing shape
Establish rectangular coordinate system when state in plane determined by two-arm axis, the y-axis of coordinate system be master arm on the stationary platform
The vertical line of equivalent hinge joint A, direction vertically upward, the highest that coordinate origin O can be moved on the y axis for moving platform center
Point, O ' are fixed platform central point；
Step 3: four kinds of peculair motion poses of master arm and slave arm are determined in coordinate system:
Pose (1): moving platform center movement to B:{-(ρorder+re), 0 }, two-arm hinge joint is located at D at this time1, and have ∠
D1BO=αmin；
Pose (2): moving platform center movement to C:{-(ρorder+re) ,-h }, two-arm hinge joint is located at D at this time2, and have D2
It is δ to y-axis distance；
Pose (3): moving platform center movement to coordinate origin O, two-arm hinge joint is located at D at this time3, and have two-arm angle most
It is small；
Pose (4): moving platform center movement to B ': { (ρorder-re), 0 }, two-arm hinge joint is located at D at this time4, slave arm
Inclination angle is maximum；
Step 4: joined according to the Delta robot architecture that desired workplace design can overcome universal joint corner to limit
Number, detailed solution process are as follows:
Step1 inputs parameter δ, αmin、re、ρorder、h、βmaxValue calculates slave arm value interval [lmin,lmax], in which:lmax=lmin+h；
Step2 assigns initial value to iteration variable
Step3 calculates D according to l1、D2Coordinate, and reject all y2> y1Point；
According to B point coordinate, the minimum angle-of-incidence α of driven arm lengths and slave armminD can be found out1Point coordinate are as follows:
{x1,y1}={ lcos αmin-ρorder-re,lsinαmin}
D can be found out according to C point coordinate and driven arm lengths2Point coordinate are as follows:
Due to D2Point is the minimum point in two-arm hinge joint motion process, therefore should reject the case where being unsatisfactory for this condition,
Implementation strategy is as follows:
If y2> y1, then l is enabledmax=l returns to Step2；
Step4 calculates equivalent hinge joint ordinate and active arm lengths, line number of going forward side by side Data preprocess；
According to D1、D2On the same circle using A point as the center of circle, A point ordinate and corresponding active at this time can be calculated
Arm lengths L, calculation formula are as follows:
Following pretreatment is done according to result above:
If L+ya≤ l, then enable lmin=l returns to Step2；
If L+l≤ya, then l is enabledmax=l returns to Step2；
Step5 calculates the minimum angle of two-arm, and judges whether to meet the limitation of universal joint corner；
Master arm and slave arm when moving to pose (3) according to two-arm have minimum angle to acquire corresponding minimum angle meter
Calculate formula are as follows:
The hinged seat of universal joint one end is vertically mounted on master arm, and the other end connects slave arm, since its corner limits
So that limited from two-arm angular range, it is therefore desirable to be handled as follows to required minimum angle:
IfThen enable lmax=l returns to Step2；
IfThen enable lmin=l returns to Step2；
IfThen stop iteration, current L, l are to meet the master arm of desired working space and driven
Brachium angle value, yaAs required z0Value；
Step6 calculates the maximum value of slave arm pivot angle γ according to iteration result
Step7 calculates slave arm maximum inclination angle alphamax, then acquire mounted angle α of the universal joint on moving platformm；
When two-arm moves to pose (4), the inclination angle of slave arm is maximum, first finds out equivalent hinge joint at this time into moving platform
Then the distance il of the heart acquires the maximum inclination angle alpha of slave armmax, universal joint is finally acquired according to inclination maximum and minimum angle-of-incidence and is existed
Mounted angle α on moving platformm, calculating process is as follows:
To sum up, the Delta robot that universal joint is used according to the design of above-mentioned calculated result, in addition to known parameters, master arm
Length is taken as L, and driven arm lengths are taken as l, and mounted angle of the universal joint on moving platform takes αm, moving platform center is in basis coordinates system
Under z-axis coordinate minimum value be taken as z0, the maximum pendulum angle of slave arm is set as γmax, obtained Delta robot can overcome ten thousand
It is limited to the corner of section, meets expectation working space.
Technical effect of the invention: it is smaller to Delta robot working space that the present invention overcomes universal joint angle ranges
Influence.According to desired working space parameter, the angle range parameter of universal joint and the part of Delta robot are set in advance
Fixed parameter can solve the Delta robot architecture's parameter for meeting design requirement, simultaneously by the way of iterative solution
Design method of structural parameters proposed by the invention, is solved using iterative manner, is easily programmed realization.
Detailed description of the invention
Scheme [1] to scheme using the Delta robot architecture of universal joint；
Scheme [2] master arm and slave arm passes through universal joint articulated figure；
Scheme [3] slave arm and moving platform passes through universal joint articulated figure；
Scheme [4] universal joint scheme of installation；
Scheme [5] universal joint angle range schematic diagram；
Scheme [6] spherical hinge angle range schematic diagram；
Scheme [7] motion pose schematic diagram；
Scheme [8] structural parameters and solves flow chart；
In figure: 1- fixed platform；2- motion platform B；3- master arm；4- slave arm；5- universal joint；
Specific embodiment
The invention will be described in further detail with reference to the accompanying drawing:
A kind of Delta robot architecture's Parameters design for overcoming universal joint corner to limit, as shown in Figure 1 to Figure 3, this
Delta robot in invention using universal joint includes fixed platform 1, there is motion platform 2, fixed platform 1 below fixed platform 1
It is connect with motion platform 2 by three groups of actuating arms, actuating arm is made of master arm 3 and slave arm 4, and the connection of 3 upper end of master arm is solid
Fixed platform 1, lower end connect slave arm 4, master arm 3 are terminated on slave arm 4, and lower end connects motion platform 2, is made using universal joint 5
For the articulation piece between master arm 3 and slave arm 4 and slave arm 4 and moving platform 2.
As shown in figure 4, being the scheme of installation of universal joint 5.In hinged master arm 3 and slave arm 4,5 one end of universal joint
Hinged seat is vertically mounted on 3 end of master arm, and other end hinged seat is mounted on 4 end of slave arm, in pivotal motion platform 2 and driven
When arm 4,5 one end hinged seat of universal joint is mounted on 4 end of slave arm, and other end hinged seat is with inclination alphamIt is mounted on motion platform 2
On.In figureFor two-arm angle, β is 4 radial angle of slave arm, and α is 4 inclination angle of slave arm.
As shown in Figure 5 to Figure 6, the respectively angle range schematic diagram of universal joint 5 and spherical hinge.The corner model of universal joint 5
Enclose the cone angle space for 90 °, and the angle range of spherical hinge is the cone angle space close to 180 °, therefore conventionally employed spherical hinge
Delta robot two-arm angle(0 °, 180 °) can be reached substantially with the variation range of slave arm inclination alpha, robot
Working space is not influenced substantially by spherical hinge angle range, and uses the movement of the Delta robot corresponding angle of universal joint
Range is relatively small, and working space is affected by universal joint angle range.
Overcome Delta robot architecture's Parameters design of above-mentioned universal joint corner limitation, comprising the following steps:
Step 1: the known parameters and parameter to be designed of clear Delta robot, it is known that parameter includes:
ρorder: it is expected the radius of working space；
H: it is expected the height of working space；
re: the equivalent hinge joint of master arm is away from fixed platform centre distance；
δ: the shortest distance of two-arm hinge joint to y-axis；
αmin: slave arm minimum angle-of-incidence；
βmax: slave arm radial angle maximum value (determines) according to universal joint；
Structural parameters to be designed include:
L: boom length；
L: active arm lengths；
αm: mounted angle of the universal joint on moving platform；
z0: moving platform center z-axis coordinate minimum value under basis coordinates system；
γmax: slave arm maximum pendulum angle；
Step 2: establish rectangular coordinate system: choosing wherein one group of master arm and slave arm is object, in slave arm without swing
Rectangular coordinate system is established in plane determined by two-arm axis when state.
As shown in fig. 7, the y-axis of coordinate system was the vertical line of master arm equivalent hinge joint A on the stationary platform, direction is vertical
Upwards, the highest point that coordinate origin O can be moved on the y axis for moving platform center, O ' are fixed platform central point；
Step 3: four kinds of peculair motion poses of master arm and slave arm are determined in coordinate system:
Pose (1): moving platform center movement to B:{-(ρorder+re), 0 }, two-arm hinge joint is located at D at this time1, and have ∠
D1BO=αmin；
Pose (2): moving platform center movement to C:{-(ρorder+re) ,-h }, two-arm hinge joint is located at D at this time2, and have D2
It is δ to y-axis distance；
Pose (3): moving platform center movement to coordinate origin O, two-arm hinge joint is located at D at this time3, and have two-arm angle most
It is small；
Pose (4): moving platform center movement to B ': { (ρorder-re), 0 }, two-arm hinge joint is located at D at this time4, slave arm
Inclination angle is maximum；
Step 4: joined according to the Delta robot architecture that desired workplace design can overcome universal joint corner to limit
Number, as shown in figure 8, detailed solution process is as follows:
Step1 inputs parameter δ, αmin、re、ρorder、h、βmaxValue calculates slave arm value interval [lmin,lmax], in which:lmax=lmin+h；
Step2 assigns initial value to iteration variable
Step3 calculates D according to l1、D2Coordinate, and reject all y2> y1Point；
According to B point coordinate, the minimum angle-of-incidence α of driven arm lengths and slave armminD can be found out1Point coordinate are as follows:
{x1,y1}={ lcos αmin-ρorder-re,lsinαmin}
D can be found out according to C point coordinate and driven arm lengths2Point coordinate are as follows:
Due to D2Point is the minimum point in two-arm hinge joint motion process, therefore should reject the case where being unsatisfactory for this condition,
Implementation strategy is as follows:
If y2> y1, then l is enabledmax=l returns to Step2；
Step4 calculates equivalent hinge joint ordinate and active arm lengths, line number of going forward side by side Data preprocess；
According to D1、D2On the same circle using A point as the center of circle, A point ordinate and corresponding active at this time can be calculated
Arm lengths L, calculation formula are as follows:
Following pretreatment is done according to result above:
If L+ya≤ l, then enable lmin=l returns to Step2；
If L+l≤ya, then l is enabledmax=l returns to Step2；
Step5 calculates the minimum angle of two-arm, and judges whether to meet the limitation of universal joint corner；
Master arm and slave arm when moving to pose (3) according to two-arm have minimum angle to acquire corresponding minimum angle meter
Calculate formula are as follows:
The hinged seat of universal joint one end is vertically mounted on master arm, and the other end connects slave arm, since its corner limits
So that limited from two-arm angular range, it is therefore desirable to be handled as follows to required minimum angle:
IfThen enable lmax=l returns to Step2；
IfThen enable lmin=l returns to Step2；
IfThen stop iteration, current L, l are to meet the master arm of desired working space and driven
Brachium angle value, yaAs required z0Value；
Step6 calculates the maximum value of slave arm pivot angle γ according to iteration result
Step7 calculates slave arm maximum inclination angle alphamax, then acquire mounted angle of the universal joint on moving platform；
When two-arm moves to pose (4), the inclination angle of slave arm is maximum, can first find out equivalent hinge joint at this time and put down to dynamic
Then the distance at platform center acquires the inclination maximum of slave arm, finally acquire universal joint according to inclination maximum and minimum angle-of-incidence and exist
Mounted angle α on moving platformm, calculating process is as follows:
To sum up, the Delta robot that universal joint is used according to the design of above-mentioned calculated result, in addition to known parameters, master arm
Length is taken as L, and driven arm lengths are taken as l, and mounted angle of the universal joint on moving platform takes αm, moving platform center is in basis coordinates system
Under z-axis coordinate minimum value be taken as z0, the maximum pendulum angle of slave arm is set as γmax, obtained Delta robot can overcome ten thousand
It is limited to the corner of section, meets expectation working space.The above content is combine specific embodiment it is made for the present invention into
One step is described in detail, and it cannot be said that a specific embodiment of the invention is only limitted to this, for the general of the technical field of the invention
For logical technical staff, without departing from the inventive concept of the premise, several simple deduction or replace can also be made, are all answered
Scope of patent protection is determined by the claims submitted when being considered as belonging to the present invention.
Claims (1)
1. a kind of Delta robot architecture's Parameters design for overcoming universal joint corner to limit, which is characterized in that including following
Step:
Step 1: according to the explicitly known parameter of the predetermined parameter of the expectation working space parameter of Delta robot and part
And parameter to be related to, it is known that parameter includes:
ρorder: it is expected the radius of working space；
H: it is expected the height of working space；
re: the equivalent hinge joint of master arm is away from silent flatform centre distance；
δ: the shortest distance of two-arm hinge joint to y-axis；
αmin: slave arm minimum angle-of-incidence；
βmax: slave arm radial angle maximum value；
Structural parameters to be designed include:
L: driven arm lengths；
L: active arm lengths；
αm: mounted angle of the universal joint on moving platform；
z0: z-axis coordinate minimum value of the moving platform center under basis coordinates system；
γmax: slave arm maximum pendulum angle；
Step 2: rectangular coordinate system is established: using wherein one group of master arm and slave arm as object, when slave arm is without swing state
Rectangular coordinate system is established in plane determined by two-arm axis, the y-axis of coordinate system was equivalent hinge of the master arm on silent flatform
The vertical line of contact A, direction vertically upward, the highest point that coordinate origin O can be moved on the y axis for moving platform center, O '
For silent flatform central point；
Step 3: four kinds of peculair motion poses of master arm and slave arm are determined in coordinate system:
Pose 1: moving platform center movement to B:{-(ρorder+re), 0 }, two-arm hinge joint is located at D at this time1, and have ∠ D1BO=
αmin；
Pose 2: moving platform center movement to C:{-(ρorder+re) ,-h }, two-arm hinge joint is located at D at this time2, and have D2To y-axis away from
From for δ；
Pose 3: moving platform center movement to coordinate origin O, two-arm hinge joint is located at D at this time3, and have two-arm angle minimum；
Pose 4: moving platform center movement to B ': { (ρorder-re), 0 }, two-arm hinge joint is located at D at this time4, slave arm inclination angle is most
Greatly；
Step 4: the Delta robot architecture's parameter that universal joint corner can be overcome to limit according to desired workplace design, in detail
Thin solution procedure is as follows:
Step1 inputs parameter δ, αmin、re、ρorder、h、βmaxValue calculates slave arm value interval [lmin,lmax], in which:lmax=lmin+h；
Step2 assigns initial value to iteration variable
Step3 calculates D according to l1、D2Coordinate, and reject all y2>y1Point；
According to B point coordinate, the minimum angle-of-incidence α of driven arm lengths and slave armminD can be found out1Point coordinate are as follows: { x1,y1}=
{lcosαmin-ρorder-re,lsinαmin}
D can be found out according to C point coordinate and driven arm lengths2Point coordinate are as follows:
Due to D2Point is the minimum point in two-arm hinge joint motion process, therefore should reject the case where being unsatisfactory for this condition, executes plan
It is slightly as follows:
If y2>y1, then l is enabledmax=l returns to Step2；
Step4 calculates equivalent hinge joint ordinate and active arm lengths, line number of going forward side by side Data preprocess；
According to D1、D2On the same circle using A point as the center of circle, A point ordinate and at this time corresponding active brachium can be calculated
L is spent, calculation formula is as follows:
Following pretreatment is done according to result above:
If L+ya≤ l, then enable lmin=l returns to Step2；
If L+l≤ya, then l is enabledmax=l returns to Step2；
Step5 calculates the minimum angle of two-arm, and judges whether to meet the limitation of universal joint corner；
Master arm and slave arm minimum angle when moving to pose 3 according to two-arm acquire corresponding minimum angle calculation formula
Are as follows:
The hinged seat of universal joint one end is vertically mounted on master arm, the other end connect slave arm, due to its corner limit so that
It is limited from two-arm angular range, it is therefore desirable to which that required minimum angle is handled as follows:
IfThen enable lmax=l returns to Step2；
IfThen enable lmin=l returns to Step2；
IfThen stop iteration, current L, l are the master arm and driven brachium for meeting desired working space
Angle value, yaAs required z0Value；
Step6 calculates the maximum value of slave arm pivot angle γ according to iteration result
Step7 calculates slave arm maximum inclination angle alphamax, then acquire mounted angle α of the universal joint on moving platformm；
When two-arm moves to pose 4, the inclination angle of slave arm is maximum, first find out at this time equivalent hinge joint to moving platform center away from
From η, the maximum inclination angle alpha of slave arm is then acquiredmax, universal joint is finally acquired in moving platform according to inclination maximum and minimum angle-of-incidence
On mounted angle αm, calculating process is as follows:
The Delta robot of universal joint is used according to the design of above-mentioned calculated result, in addition to known parameters, active arm lengths are taken as L,
Driven arm lengths are taken as l, and mounted angle of the universal joint on moving platform takes αm, z-axis seat of the moving platform center under basis coordinates system
Mark minimum value is taken as z0, the maximum pendulum angle of slave arm is set as γmax, obtained Delta robot can overcome the corner of universal joint
Limitation meets expectation working space.
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| CN102029614A (en) * | 2011-01-24 | 2011-04-27 | 哈尔滨工业大学 | Three-degree-of-freedom spherical space robot wrist |
| CN103341865A (en) * | 2013-07-05 | 2013-10-09 | 大连理工大学 | Three-freedom-degree constant speed decoupling space robot active spherical wrist and universal compliant control method |
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| CN102029614A (en) * | 2011-01-24 | 2011-04-27 | 哈尔滨工业大学 | Three-degree-of-freedom spherical space robot wrist |
| CN103341865A (en) * | 2013-07-05 | 2013-10-09 | 大连理工大学 | Three-freedom-degree constant speed decoupling space robot active spherical wrist and universal compliant control method |
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