Not Available in v2: The Rotatable Cartesian arm solution has been removed in Smoothieware v2 and is not available. If you need this functionality, you must use Smoothieware v1 or consider alternative approaches such as rotating your G-code coordinates before sending them to the machine.

Rotatable Cartesian Arm Solution

Version Support: This arm solution is only supported in Smoothieware v1 ✅. It has been removed in v2 ❌

Rotatable Cartesian is a variant of the standard Cartesian arm solution that allows you to rotate the entire coordinate system by a specified angle.

This is useful when your machine’s physical frame is not aligned with the desired working coordinate system, or when you want to work at an angle without physically rotating your workpiece or machine.

What is Rotatable Cartesian?

In a standard Cartesian system, the X, Y, and Z axes are fixed relative to the machine’s frame. The Rotatable Cartesian solution applies a rotation transformation to the X-Y plane, effectively rotating your coordinate system by a specified angle.

Key characteristics:

The Z axis remains vertical (no rotation in Z)
The X and Y axes are rotated in the horizontal plane by the specified angle
All G-code coordinates are automatically transformed to the rotated frame
Each motor still controls a single linear axis (unlike CoreXY)

Mathematical Transformation

The rotatable cartesian solution applies a 2D rotation matrix to the X and Y coordinates:

Alpha position = cos(angle) × X - sin(angle) × Y
Beta position  = sin(angle) × X + cos(angle) × Y
Gamma position = Z (unchanged)

Where angle is the rotation angle specified in the configuration (converted from degrees to radians).

When to Use Rotatable Cartesian

Rotatable Cartesian is useful in specific scenarios:

Misaligned Machines: Your machine frame is built at an angle, but you want to work in a standard X/Y coordinate system
Angled Workpieces: You have a workpiece mounted at an angle and want to mill/cut along its natural axes
Workspace Optimization: You want to maximize usable workspace when your machine is positioned at an angle to your work table
Calibration Compensation: Your machine has a slight angular misalignment that you want to correct in software

Alternative Approaches: In most cases, it's better to physically align your machine or rotate your G-code coordinates before sending them to the machine. The Rotatable Cartesian solution is primarily useful for permanent angular misalignments that cannot be easily corrected mechanically.

Configuration

To configure your machine to use the Rotatable Cartesian arm solution, add this to your configuration file:

arm_solution rotatable_cartesian

Angle Parameter

The rotation angle is specified using the alpha_angle parameter:

alpha_angle    45.0    # Rotation angle in degrees (default: 0.0)

Important notes:

The angle is specified in degrees (not radians)
Default value is 0.0 degrees (which makes it equivalent to standard Cartesian)
Positive angles rotate counter-clockwise when viewed from above (looking down at the X-Y plane)
The angle is applied to the entire coordinate system

Complete Configuration Example

# Rotatable Cartesian arm solution
arm_solution                                 rotatable_cartesian
alpha_angle                                  30.0    # Rotate coordinate system 30° counter-clockwise

# Alpha (X motor)
alpha_step_pin                               2.0
alpha_dir_pin                                0.5
alpha_en_pin                                 0.4
alpha_steps_per_mm                           80
alpha_max_rate                               12000

# Beta (Y motor)
beta_step_pin                                2.1
beta_dir_pin                                 0.11
beta_en_pin                                  0.10
beta_steps_per_mm                            80
beta_max_rate                                12000

# Gamma (Z motor)
gamma_step_pin                               2.2
gamma_dir_pin                                0.20
gamma_en_pin                                 0.19
gamma_steps_per_mm                           400
gamma_max_rate                               6000

v1 Only: This configuration section applies only to Smoothieware v1. The Rotatable Cartesian arm solution is not available in v2. Please see the Migration to Smoothieware v2 section for alternatives.

Understanding the Rotation

Example: 45-Degree Rotation

If you set alpha_angle 45.0:

A command to move to X10 Y0 would result in the toolhead moving to approximately X7.07 Y7.07 in machine coordinates
A command to move to X0 Y10 would result in the toolhead moving to approximately X-7.07 Y7.07 in machine coordinates
The Z axis remains unchanged

Coordinate System Visualization

Standard Cartesian (alpha_angle = 0):
      Y
      ^
      |
      |
      +------> X

Rotated Cartesian (alpha_angle = 45):
       Y (rotated)
      ╱
     ╱
    ╱
   +------> X (rotated)

Common Use Cases

Case 1: Machine Built at an Angle

Your machine frame was built with the gantry at 15° to your work table:

arm_solution rotatable_cartesian
alpha_angle  15.0    # Compensate for 15° misalignment

Now when you command X100 Y0, the machine will move 100mm along your work table’s X direction, even though the gantry is angled.

Case 2: Diamond-Oriented Workspace

Your machine is positioned at 45° to maximize diagonal workspace:

arm_solution rotatable_cartesian
alpha_angle  45.0    # Rotate to diamond orientation

Case 3: Small Angular Calibration

Your machine has a 2° misalignment that’s difficult to correct mechanically:

arm_solution rotatable_cartesian
alpha_angle  2.0    # Small correction angle

v1 Only: These configuration examples apply only to Smoothieware v1. For v2 alternatives, see the Migration to Smoothieware v2 section.

Migration to Smoothieware v2

Not Available in v2: The Rotatable Cartesian arm solution has been removed in Smoothieware v2. If you need similar functionality in v2, you have several alternatives:

Rotate G-code before sending: Use your CAM software or a post-processor to rotate coordinates
Use coordinate system offsets: G-code coordinate system commands (G54-G59) can sometimes achieve similar results
Physically align your machine: Mechanically correct the angular misalignment
Stay on v1: If this feature is critical, continue using Smoothieware v1

Troubleshooting

Problem: Movement directions are unexpected

Solution: Remember that the rotation is counter-clockwise when viewed from above. If movements seem reversed, try using a negative angle instead of positive (e.g., use -30 instead of 330).

Problem: Movements are correct but distances are wrong

Solution: Check your alpha_steps_per_mm and beta_steps_per_mm settings. The rotation transformation doesn’t change distances, only directions.

Problem: Homing doesn’t work correctly

Solution: Endstops are still in machine coordinates (not rotated). Make sure your endstop positions match your machine’s physical axes, not the rotated coordinate system.

Comparison with Other Solutions

Feature	Rotatable Cartesian	Standard Cartesian	CoreXY
Coordinate rotation	Yes	No	No
Motors per axis	1:1 mapping	1:1 mapping	Coupled X/Y
Complexity	Low	Very low	Medium
v1 Support	Yes	Yes	Yes
v2 Support	No	Yes	Yes

Source Code

For developers or those interested in the implementation details, the Rotatable Cartesian solution is implemented in:

v1: RotatableCartesianSolution.cpp