Kinematics Examples

An example of non-orthogonal dual table machine is shown below:

 

 

An example of the new kinematics parameters of a non-orthogonal dual table machine:

Parameter

mom Variable

t0

mom_kin_spindle_axis (0,0,1)

p

mom_kin_4th_axis_vector (1,0,1)

s

mom_kin_5th_axis_vector (0,0,1)

cp

mom_kin_4th_axis_point (2,-2,-10)

cs

mom_kin_5th_axis_point (4,0,-4)

m0

mom_kin_machine_zero_offset (1,10,0)

 

The purpose of these variables is to define the kinematics of the machine, so they are referred to as Kinematic Parameters. All the kinematic parameters are defined at the initial (zero) position of the machine, which is the position of the machine tool when all linear slide variables and all rotary angles are set to zero. All the kinematic parameters (points and vectors) are expressed in the Machine Tool Coordinate System (MTCS), which is a fixed coordinate system that has its axes parallel to the linear slides of the machine tool and its origin at the machine gauge point at zero (initial) position. The direction of the MTCS’ axes is selected in such a way that all axes moving the tool (spindle) are identical with the direction of the MTCS, and all axes moving the part (table) are opposite to the direction of the MTCS. By this rule, the observer standing on the table will see the spindle (tool) moving in the accordance with the sign of linear slide variables.

The similar rule is applied to the vectors rotary axes. They will follow a standard right-hand rule (in a closed right hand fist the thumb shows the direction of the vector, the four remaining fingers point into a counter-clockwise direction of rotation) for the rotary axes moving the tool (spindle), and have their direction reversed for the rotary axes in table. This way the observer standing on the table will see the positive direction of the spindle rotary motion as counter-clockwise.

The direction of the machine spindle axis, as well as the head spindle axis, is always assumed to be from tool tip to the tool mounting point.

The Head parameters described in section 3.1 are also expressed in the MTCS.

Some examples of the new kinematic parameters are shown below (the MTCS is shown in blue).

An example of the new kinematic parameters defined at zero (initial) position of a dual head machine:

 

Parameter

mom Variable

t0

mom_kin_spindle_axis (0,0,1)

p

mom_kin_4th_axis_vector (1,0,0)

s

mom_kin_5th_axis_vector (0,1,0)

cp

mom_kin_4th_axis_point (4,0,4)

cs

mom_kin_5th_axis_point (0,3,4)

m0

mom_kin_machine_zero_offset (4,0,-10)

 

An example of the new mom kinematic parameters defined at zero (initial) position of a head-table machine.

Parameter

mom Variable

t0

mom_kin_spindle_axis (0,0,1)

p

mom_kin_4th_axis_vector (0,-1,0)

s

mom_kin_5th_axis_vector (0,0,1)

cp

mom_kin_4th_axis_point (-1,-1,1)

cs

mom_kin_5th_axis_point (10,0,-10)

m0

mom_kin_machine_zero_offset (14,0,-2)

 

An example of the new kinematic parameters defined at zero (initial) position of a dual table machine:

Parameter

mom Variable

t0

mom_kin_spindle_axis (-1,0,0)

p

mom_kin_4th_axis_vector (0,-1,0)

s

mom_kin_5th_axis_vector (0,0,1)

cp

mom_kin_4th_axis_point (10,-1,-10)

cs

mom_kin_5th_axis_point (8,0,-8)

m0

mom_kin_machine_zero_offset (9,4,0)