Linear Interpolation With 3º Polynomial Interpolation Connection: Type 1

At a Glance

This type of interpolation can be used to link linear segments by smoothing transitions using 3º interpolation.

The trajectory does not pass through the point defined in the table but follows a curve defined by the parameters. The smaller the connection zone, the closer the trajectory will be to the point, although the larger the curve will be, thus reducing the maximum possible speed.

Illustration

The diagram below illustrates an example of a type 1 segment:

Block Parameters

The table below indicates the parameters to be entered in the trajectory table for this type of segment:

Parameter	Description
ParW0	Enter 1 to indicate that the type of interpolation to be used is linear interpolation with 3° polynomial interpolation connection.
ParW1 = NpLin	Indicate the number of points in the linear part of the segment in this parameter. This number of points (minimum 1) represents the number of intermediate points that the module has to calculate in order to define the trajectory on this linear part.
ParW2 = NpRacc	Indicate the number of points in the cubic interpolation part of the segment in this parameter. This number of points (minimum 1) represents the number of intermediate points that the module has to calculate in order to define the trajectory on this part. It should be enough to ensure precision of the trajectory, and a minimum value of 15 is recommended.
ParW3 = KF	3° interpolation shape coefficient. Between 50 and 200 this coefficient can be used to modify the shape of the connection zone. The default value is 100, and it is advisable to keep this default value if the desired movement allows, as it ensures that there will not be any motion "overshoot". Note: The more the KF coefficient increases, the nearer the curve comes to the segment characteristic point, and the more it decreases, the further away the curve goes.
ParW4	For this type of segment, only tangent mode can be used. If a third tangent type axis is being used, select tangent mode (bit 8 of ParW4 at 1) to indicate that the motion of the third axis will follow the curve using tangent mode (positioning a tool for example so that it is always at right-angles to the curve and follows its tangent). Note: Tangent mode (bit 8 at 1) will be available in a later version of the TjE/TSX CSY 85 combination, but for the moment only angular positioning of the third Z axis is supported. For a movement on two axes, enter the value 0.
ParF1 = lracc1 ParF2 = lracc2	lracc1 is the length of the initial connection. lracc2 is the length of the final connection. lracc1 and lracc2, expressed in mm, determine the length of the interpolation zone. If these lengths are too long (for example lracc1 > distance between the current point (Pn) and the previous point (Pn-1)), the maximum possible length should be used. This maximum length is automatically calculated by the module according to the previous section for lracc1 and the next section for lracc2. Example: If the sum of lracc2 of Pn-1 and lracc1 of Pn is greater than the distance between Pn-1 and Pn, the linear part of the trajectory will resume at a reversal point on the trajectory between these two points. In addition if lracc1 > 2lracc2 then interpolation considers that lracc1=2lracc2 Similarly if lracc2 > 2lracc1 then interpolation considers that lracc2=2lracc1

Error Codes

When this type of segment is used, the error codes that can be returned in word %MWr.m.c.3 are as follows:

Code	Description
9501	One of the lengths lracc1 or lracc2 equals zero (illegal scenario).
9504	The table contains two consecutive identical points.
9514	Link too long: Next segment = 0
9515	The number of points in the linear segment is set to 0.
9516	The number of points in the 3º polynomial interpolation segment is set to 0.

NOTE: The error codes indicated are those for the TSX CSY 85 module. The error codes for TjE are the same but without the 9 (9501 corresponds to 501 etc).

Shape Coefficient KF

The diagram below illustrates how the shape of the trajectory changes depending on the value of the shape coefficient KF (between 50 and 200):

NOTE: The more the KF coefficient increases, the nearer the curve comes to the segment characteristic point, and the more it decreases, the further away the curve goes.

Example Trajectory

The diagram below illustrates an example of a trajectory using type 1 segments: