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<title>Kinematics Examples</title>

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<p class=EndLine>&nbsp;</p>

<h1 style="background-image: url(paper.gif);">Kinematics Examples</h1>

<p>An example of non-orthogonal dual table machine is shown below:</p>

<p>&nbsp;</p>

<p class=Image><img src="graphics/kin_5.gif"
					x-maintain-ratio=true
					style="border: none;
							width: 355px;
							height: 430px;
							float: none;"
					width=355
					height=430
					border=0></p>

<p class=Paragraph>&nbsp;</p>

<p class=Paragraph>An example of the new kinematics parameters of a non-orthogonal 
 dual table machine:</p>

<!--(Table)=========================================================-->
<table x-use-null-cells
		style="x-cell-content-align: top; border-spacing: 3px;"
		cellspacing=3>
<col>
<col>

<tr valign=top>
<td colspan=1
	rowspan=1
	style="padding-right: 10px;
			padding-left: 10px;
			border-left-style: none;
			border-top-style: none;
			border-right-style: none;
			border-bottom-style: none;
			background-color: #c0c0c0;"
	bgcolor=#C0C0C0>
<p class=CellTopic>Parameter</td>
<td colspan=1
	rowspan=1
	style="padding-right: 10px;
			padding-left: 10px;
			border-top-style: none;
			border-right-style: none;
			border-bottom-style: none;
			background-color: #c0c0c0;"
	bgcolor=#C0C0C0>
<p class=CellTopic>mom Variable</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>t0 </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_spindle_axis (0,0,1)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>p </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=Paragraph>mom_kin_4th_axis_vector (1,0,1)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>s </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_5th_axis_vector (0,0,1)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>cp</td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=Paragraph>mom_kin_4th_axis_point (2,-2,-10)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>cs </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=Paragraph>mom_kin_5th_axis_point (4,0,-4)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-right-style: none;
			border-left-style: none;
			border-bottom-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>m0 </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=Paragraph>mom_kin_machine_zero_offset (1,10,0)</td></tr>
</table>

<p class=Paragraph>&nbsp;</p>

<p>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. </p>

<p>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. </p>

<p>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. 
 </p>

<p>The Head parameters described in section 3.1 are also expressed in the 
 MTCS.</p>

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

<p class=Image><img src="graphics/kin_2.gif"
					x-maintain-ratio=true
					style="border: none;
							width: 467px;
							height: 409px;
							float: none;"
					width=467
					height=409
					border=0></p>

<p class=Paragraph>An example of the new kinematic parameters defined at 
 zero (initial) position of a dual head machine:</p>

<p class=Paragraph>&nbsp;</p>

<!--(Table)=========================================================-->
<table x-use-null-cells
		style="x-cell-content-align: top; border-spacing: 3px;"
		cellspacing=3>
<col>
<col>

<tr valign=top>
<td colspan=1
	rowspan=1
	style="padding-right: 10px;
			padding-left: 10px;
			border-left-style: none;
			border-top-style: none;
			border-right-style: none;
			border-bottom-style: none;
			background-color: #c0c0c0;"
	bgcolor=#C0C0C0>
<p class=CellTopic>Parameter</td>
<td colspan=1
	rowspan=1
	style="padding-right: 10px;
			padding-left: 10px;
			border-top-style: none;
			border-right-style: none;
			border-bottom-style: none;
			background-color: #c0c0c0;"
	bgcolor=#C0C0C0>
<p class=CellTopic>mom Variable</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>t0 </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_spindle_axis (0,0,1)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>p </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=Paragraph>mom_kin_4th_axis_vector (1,0,0)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>s </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_5th_axis_vector (0,1,0)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>cp</td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_4th_axis_point (4,0,4)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>cs </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=Paragraph>mom_kin_5th_axis_point (0,3,4)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-right-style: none;
			border-left-style: none;
			border-bottom-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>m0 </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_machine_zero_offset (4,0,-10)</td></tr>
</table>

<p class=Image>&nbsp;</p>

<p class=Image><img src="graphics/kin_3.gif"
					x-maintain-ratio=true
					style="border: none;
							width: 447px;
							height: 430px;
							float: none;"
					width=447
					height=430
					border=0></p>

<p class=Paragraph>An example of the new mom kinematic parameters defined 
 at zero (initial) position of a head-table machine. </p>

<!--(Table)=========================================================-->
<table x-use-null-cells
		style="x-cell-content-align: top; border-spacing: 3px;"
		cellspacing=3>
<col>
<col>

<tr valign=top>
<td colspan=1
	rowspan=1
	style="padding-right: 10px;
			padding-left: 10px;
			border-left-style: none;
			border-top-style: none;
			border-right-style: none;
			border-bottom-style: none;
			background-color: #c0c0c0;"
	bgcolor=#C0C0C0>
<p class=CellTopic>Parameter</td>
<td colspan=1
	rowspan=1
	style="padding-right: 10px;
			padding-left: 10px;
			border-top-style: none;
			border-right-style: none;
			border-bottom-style: none;
			background-color: #c0c0c0;"
	bgcolor=#C0C0C0>
<p class=CellTopic>mom Variable</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>t0 </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_spindle_axis (0,0,1)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>p </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_4th_axis_vector (0,-1,0)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>s </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_5th_axis_vector (0,0,1)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>cp</td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_4th_axis_point (-1,-1,1)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>cs </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=Paragraph>mom_kin_5th_axis_point (10,0,-10)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-right-style: none;
			border-left-style: none;
			border-bottom-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>m0 </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_machine_zero_offset (14,0,-2)</td></tr>
</table>

<p class=Paragraph>&nbsp;</p>

<p class=Image><img src="graphics/kin_4.gif"
					x-maintain-ratio=true
					style="border: none;
							width: 538px;
							height: 371px;
							float: none;"
					width=538
					height=371
					border=0></p>

<p class=Paragraph>An example of the new kinematic parameters defined at 
 zero (initial) position of a dual table machine:</p>

<!--(Table)=========================================================-->
<table x-use-null-cells
		style="x-cell-content-align: top; border-spacing: 3px;"
		cellspacing=3>
<col>
<col>

<tr valign=top>
<td colspan=1
	rowspan=1
	style="padding-right: 10px;
			padding-left: 10px;
			border-left-style: none;
			border-top-style: none;
			border-right-style: none;
			border-bottom-style: none;
			background-color: #c0c0c0;"
	bgcolor=#C0C0C0>
<p class=CellTopic>Parameter</td>
<td colspan=1
	rowspan=1
	style="padding-right: 10px;
			padding-left: 10px;
			border-top-style: none;
			border-right-style: none;
			border-bottom-style: none;
			background-color: #c0c0c0;"
	bgcolor=#C0C0C0>
<p class=CellTopic>mom Variable</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>t0 </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_spindle_axis (-1,0,0)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>p </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_4th_axis_vector (0,-1,0)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>s </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_5th_axis_vector (0,0,1)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>cp</td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_4th_axis_point (10,-1,-10)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			border-left-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>cs </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_5th_axis_point (8,0,-8)</td></tr>

<tr valign=top>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-right-style: none;
			border-left-style: none;
			border-bottom-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>m0 </td>
<td style="padding-right: 10px;
			padding-left: 10px;
			border-bottom-style: none;
			border-right-style: none;
			background-color: #f4f4f4;"
	bgcolor=#F4F4F4>
<p class=CellDescrip>mom_kin_machine_zero_offset (9,4,0)</td></tr>
</table>

<p class=EndLine>&nbsp;</p>

<p class=blank>&nbsp;</p>

</body>

</html>
