Delta Robot Kinematic Module
General Kinematic Description
This robot module controls the special 4-degree-of-freedom parallel geometry mechanism called the "Delta" robot. Unlike the more common serial-geometry mechanisms, all three of the primary actuators of this parallel mechanism work together to produce the three Cartesian translation degrees-of-freedom. A fourth conventional rotary motor is added to control the fourth, theta, degree-of-freedom.
The three primary actuators of this mechanism can be implemented using rack and pinion drives or by employing geared rotary drives.
Module Specifications
Minimum V+ Compatibility
V+ 11.2 or later for rack and pinion drives
V+ 13.1E5 or later for geared rotary drives
V+ 15 or later for rack and pinion with L3 specifiedDevice Module File Name
"dlt"
Device Module Identification Number
27
Default Startup Message
"Delta Robot Module."
Default Joint Configuration and Mapping
This robot utilizes four joints and four motors. By default, the joints and motors are mapped as follows:
Joint
Motor
Servo Board
Board Channel
1
1
1
1
2
2
1
2
3
3
1
3
4
4
1
4
Additional License requirements:
Kinematic License Adept PN 09961-00004
Robot Option Word (bit numbers start with bit #1)
Bit
Default
Description
5
off
If on, the robot’s primary actuators are geared rotary drives, otherwise, rack and pinion drives are being utilized.
Robot Model and Robot Serial Number, Default
0, 0
Specific Link Descriptions
This robot module controls a mechanism with four degrees-of-freedom. The first three degrees-of-freedom operate in parallel to control the position of the tool. The fourth degree-of-freedom rotates the tool about the Z axis. The exact description for these degrees-of-freedom are as follows:
Joints 1, 2, and 3 are identical three-link actuators. The top link of each of these joints is connected to the stationary, overhead base of the robot. Each of the top links connects to the overhead base at a point on the perimeter of a circle and pivots in a radial direction. The plane of this circle defines the X-Y world coordinate plane. The world Z coordinate is perpendicular to the plane of this circle and points up. The origin of the circle defines the origin of the world coordinate system.
The bottom of each top link is connected to the top of two rods via spherical joints. The rods in each pair remain parallel to each other and are connected at the bottom, via spherical joints, to a moving platform. The moving platform translates in three dimensions, but has a fixed orientation relative to the stationary, overhead base.
For one model of this robot, each of the three primary joints is driven by a rack and pinion drive. The pinion is fixed to a stationary motor that is positioned above the overhead base of the robot. The rack engages the pinion and is connected to the bottom of the top link of one of the primary joints. (See Figure 1.)
To simplify computation, and for ease of understanding, the position of each joint is defined by how far the pinion has driven the rack. By definition, a joint is at its zero position when the pin jointing the rack to the top link is at the same height as the pin connecting the top link to the stationary, overhead base. Each time the pinion turns one full revolution and moves the rack down, the joint position is increased by
2*rmot*PI
where rmot is the radius of the pinion. Therefore, the scale factor for each joint is equal to
2*rmot*PI/encoder_counts_per_pinion_rotation
For the second model of this robot, each of the primary joints is driven by a geared rotary motor. In this case, the joint angle corresponds to the rotation of the top link. When a motor moves the end of the top link downward, the joint is rotating in a positive direction. When the two pivot points at the ends of the top link are in the same horizontal plane, the value of the joint position is zero. (See Figure 2.)
Joint 4 is a revolute axis (theta) about the world Z direction. This theta axis is mounted on the moving platform that is driven by the three primary joints. A positive rotation of the theta joint turns the robot end effector in a negative direction relative to the world Z axis. The axis of rotation of joint 4 defines the nominal Z axis of the robot tool frame of reference. That is, if a NULL tool is defined, the Z axis of the tool frame will be collinear with the axis of rotation of joint 4 and will be pointed in the direction of the negative world Z axis.
As with all robot modules, the standard V+ BASE and TOOL transformations can be used in combination with the geometric model to specify and compute the end point of the robot relative to the world coordinate frame.
Variations in Axis Configuration
This module controls all four axes as defined above and cannot be reconfigured for any other number of axes. However, as previously noted, the primary motor drives can either be implemented with rack and pinions or geared rotary motors.
Link Dimensions (Geometric Dimensional Constants)
There are a total of 13 dimensional constants that must be defined to specify the geometric transformations performed by this module. The first 4 constants define the fundamental geometry of the three identical three-link primary joints. The next 5 constants define the geometry of the rack and pinion drive. These constants can be set to any value when geared drives are utilized. The next three constants define how the primary joints are positioned around the stationary overhead base. The last constant defines a moment arm for the rack and pinion drive. The definitions for all 13 of these dimensions are illustrated in accompanying figures.
Interpretation of Cartesian Rotations
During program-generated straight-line motions, the first Cartesian rotation speed controls the rate at which joint 4 rotates, and the speed should be set to be consistent with the joint-interpolated speed for joint 4. No other Cartesian rotational speeds are applicable.
Coupling Between Robot Joints and Motors
This robot module does not support any coupling between any of the axes (other than that which is an intrinsic characteristic of the parallel geometry).
Robot Configuration Control Program Instructions
The following robot configuration-control program instructions do not have any effect upon the operation of mechanisms controlled by this module:
ABOVE, BELOW, FLIP, NOFLIP, LEFTY, RIGHTY
Special Features
ROBOT.OPR is a general-purpose instruction, whose interpretation varies from one robot module to another.
For this robot module, this instruction sets the Cartesian acceleration parameters to one of three sets of values. The purpose of this operation is to adjust the robot's dynamic performance depending upon the payload being carried by the robot.
The general syntax for this instruction is:
ROBOT.OPR (function_code) exp1, exp2, ..., expn
NOTE: Any "function" value not listed below will result in an *Invalid argument* error. The same error results if an "exp" value exceeds its allowable range.
Parameter Descriptions for ROBOT.OPR
function_code
0
exp1
Number of the set of Cartesian acceleration parameters to utilize (1-3). The parameters are intended to be used as follows:
Set Payload 1 0-100 g 2 101-300 g 3 301-500 g
Additional Restrictions & Notes
None.
Figure 1: Primary Joint Dimensions for Rack and Pinion Drive
Figure 2: Primary Joint Dimensions for Geared Rotary Drive
Figure 3: Relative Positions of Primary Joints
Table 1: SPEC Link Dimensions
SPEC parameter
Label
C1000 Values
Notes
1
ra
75.0
2
rb
40.0
3
L1
230.0
4
L2
470.0
5
a
300.0
Rack and pinion only
6
c
164.2926
Rack and pinion only
7
dmot
121.5
Rack and pinion only
8
rmot
4.5
Rack and pinion only
9
psi
10.0
Rack and pinion only
10
thlg_1
0.0
11
thlg_2
120.0
12
thlg_3
240.0
13
L3
230.0
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