Renesas RAA3064002GFP, Справочное руководство

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R01AN5644EJ0100 Rev.1.00 Page 42 of 62
Jan 22, 2021
Reference Guide for a 2-Axis Robot Arm with 2-Phase Stepping
Motors Incorporating Resolvers
RX24T, RX72M,
RAA3064002GFP/RAA3064003GFP
•
Central coordinates of an arc
Calculate the central coordinates of a circle passing through three points and then calculate the radius from
the obtained central coordinates.
�
(
𝑥𝑥
1
− 𝑥𝑥𝑦𝑦
) 2
+ ( 𝑦𝑦
1
− 𝑦𝑦𝑦𝑦
) 2
= 𝑟𝑟
2
𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡𝐸𝐸𝐸𝐸𝐸𝐸 1
( 𝑥𝑥
2
− 𝑥𝑥𝑦𝑦 )
2
+ ( 𝑦𝑦
2
− 𝑦𝑦𝑦𝑦 )
2
= 𝑟𝑟
2
𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡𝐸𝐸𝐸𝐸𝐸𝐸 2
( 𝑥𝑥
3
− 𝑥𝑥𝑦𝑦 )
2
+ ( 𝑦𝑦
3
− 𝑦𝑦𝑦𝑦 )
2
= 𝑟𝑟
2
𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡𝐸𝐸𝐸𝐸𝐸𝐸 3
Calculate under the condition that equation 1 is equal to equation 2.
( 𝑥𝑥
1
− 𝑥𝑥𝑦𝑦 )
2
+ ( 𝑦𝑦
1
− 𝑦𝑦𝑦𝑦 )
2
= ( 𝑥𝑥
2
− 𝑥𝑥𝑦𝑦 )
2
+ ( 𝑦𝑦
2
− 𝑦𝑦𝑦𝑦 )
2
(
𝑥𝑥
1
+ 𝑦𝑦
1
− 2 𝑥𝑥𝑦𝑦
)(
𝑥𝑥
1
− 𝑥𝑥
2
) + (
𝑦𝑦
1
+ 𝑦𝑦
2
− 2 𝑥𝑥𝑦𝑦
)(
𝑦𝑦
1
− 𝑦𝑦
2
) = 0
Similarly, calculate under the condition that equation 2 is equal to equation 3.
�
( 𝑥𝑥
1
− 𝑥𝑥
2
) 𝑥𝑥𝑦𝑦 + ( 𝑦𝑦
1
− 𝑦𝑦
2
) 𝑦𝑦𝑦𝑦 =
1
2
{( 𝑥𝑥
1
2
− 𝑥𝑥
2
2
) + ( 𝑦𝑦
1
2
− 𝑦𝑦
2
2
)}
(
𝑥𝑥
2
− 𝑥𝑥
3
)
𝑥𝑥𝑦𝑦 + ( 𝑦𝑦
2
− 𝑦𝑦
3
)
𝑦𝑦𝑦𝑦 =
1
2
{(
𝑥𝑥
2
2
− 𝑥𝑥
3
2
) + (
𝑦𝑦
2
2
− 𝑦𝑦
3
2
)}
On the assumption of
𝑋𝑋
𝑖𝑖
= 𝑥𝑥
𝑖𝑖
2
+ 𝑦𝑦
𝑖𝑖
2 , perform substitution to form a determinant.
�
𝑥𝑥
1
− 𝑥𝑥
2
𝑦𝑦
1
− 𝑦𝑦
2
𝑥𝑥
2
− 𝑥𝑥
3
𝑦𝑦
2
− 𝑦𝑦
3
� �
𝑥𝑥𝑦𝑦
𝑦𝑦𝑦𝑦
� =
1
2
�
𝑋𝑋
1
− 𝑋𝑋
2
𝑋𝑋
2
− 𝑋𝑋
3
�
On the assumption of
�𝐸𝐸 𝑏𝑏
𝑦𝑦 𝑑𝑑�
= �
𝑥𝑥
1
− 𝑥𝑥
2
𝑦𝑦
1
− 𝑦𝑦
2
𝑥𝑥
2
− 𝑥𝑥
3
𝑦𝑦
2
− 𝑦𝑦
3
�
, calculate the inverse matrix.
�
𝑥𝑥𝑦𝑦
𝑦𝑦𝑦𝑦�
=
1
2 × 1
𝐸𝐸𝑑𝑑 − 𝑏𝑏𝑦𝑦
× � 𝑑𝑑
−𝑏𝑏
−𝑦𝑦 𝐸𝐸 �
× �
𝑋𝑋
1
− 𝑋𝑋
2
𝑋𝑋
2
− 𝑋𝑋
3
�
P
1
(x1,y1)
P
2
(x2,y2)
P
c
(xc,yc)
●
●
✖
R
P
3
(x3,y3)
●