interface

Joint definition

Definition of the different joints used for pylinkage.

class pylinkage.interface.joint.Crank(x=None, y=None, joint0=None, distance=None, angle=None, name=None)

Bases: Joint

Define a crank joint.

__init__(x=None, y=None, joint0=None, distance=None, angle=None, name=None)

Define a crank (circular motor).

Parameters

xfloat, optional

initial horizontal position, won’t be used thereafter. The default is None.

yfloat, optional

initial vertical position. The default is None.

joint0Union[Joint, tuple[float]], optional

first reference joint. The default is None.

distancefloat, optional

distance to keep between joint0 and self. The default is None.

anglefloat, optional

It is the angle (horizontal axis, joint0, self). Should be in radian and in trigonometric order. The default is None.

namestr, optional

user-friendly name. The default is None.

Returns

None.

_abc_impl = <_abc._abc_data object>
angle
get_constraints()

Return the distance to the center of rotation.

r
reload(dt=1)

Make a step of crank.

Parameters:

dt (float) – Fraction of step to do (Default value = 1)

set_anchor0(joint, distance=None)

First joint anchor and fixed distance.

Parameters:

  • joint –

  • distance – (Default value = None)

set_constraints(distance=None, *args)

Set geometric constraints, only self.r is affected.

Parameters:

  • distance (float) – Distance from the reference point. (Default value = None)

  • args – Unused, but preserves the object structure.

class pylinkage.interface.joint.Fixed(x=None, y=None, joint0=None, joint1=None, distance=None, angle=None, name=None)

Bases: Joint

Define a joint using parents locations only, with no ambiguity.

__init__(x=None, y=None, joint0=None, joint1=None, distance=None, angle=None, name=None)

Create a point, of position fully defined by its two references.

Arguments

xfloat, optional

Position on horizontal axis. The default is 0.

yfloat, optional

Position on vertical axis. The default is O.

namestr, optional

Friendly name for human readability. The default is None.

joint0Union[Joint, tuple[float]], optional

Linked pivot joint 1 (geometric constraints). The default is None.

joint1Union[Joint, tuple[float]], optional

Other pivot joint linked. The default is None.

distancefloat, optional

Distance to keep constant between joint0 and self. The default is None.

anglefloat, optional

Angle (joint1, joint0, self). Should be in radian and in trigonometric order. The default is None.

_abc_impl = <_abc._abc_data object>
angle
get_constraints()

Return the constraining distance and angle parameters.

r
reload()

Compute point coordinates.

We know point position relative to its two parents, which gives a local space. We know the orientation of local space, so we can solve the whole. Local space is defined by link[0] as the origin and (link[0], link[1]) as abscissas axis.

set_anchor0(joint, distance=None, angle=None)

First joint anchor and characteristics.

Parameters:

  • joint –

  • distance – (Default value = None)

  • angle – (Default value = None)

set_anchor1(joint)

Second joint anchor.

Parameters:

joint –

set_constraints(distance=None, angle=None)

Set geometric constraints.

Parameters:

  • distance – (Default value = None)

  • angle – (Default value = None)

class pylinkage.interface.joint.Joint(x=0, y=0, joint0=None, joint1=None, name=None)

Bases: ABC

Geometric constraint expressed by two joints.

Abstract class should always be inherited.

__init__(x=0, y=0, joint0=None, joint1=None, name=None)

Create Joint.

Arguments

xfloat, optional

Position on horizontal axis. The default is 0.

yfloat, optional

Position on vertical axis. The default is O.

namestr, optional

Friendly name for human readability. The default is None.

joint0Union[Joint, tuple[float]], optional

Linked pivot joint 1 (geometric constraints). The default is None.

joint1Union[Joint, tuple[float]], optional

Other pivot joint linked. The default is None.

_abc_impl = <_abc._abc_data object>
coord()

Return cartesian coordinates.

abstract get_constraints()

Return geometric constraints applying to this Joint.

joint0
joint1
name
abstract set_constraints(*args)

Set geometric constraints applying to this Joint.

set_coord(*args)

Take a sequence or two scalars, and assign them to object x, y.

Parameters:

args (tuple[float, float] | tuple[tuple[float, float]]) – Coordinates to set, either as two elements or as a tuple of 2 elements

x
y
class pylinkage.interface.joint.Pivot(x=0, y=0, joint0=None, joint1=None, distance0=None, distance1=None, name=None)

Bases: Joint

Center of pivot joint.

__init__(x=0, y=0, joint0=None, joint1=None, distance0=None, distance1=None, name=None)

Set point position, parents, and if it is fixed for this turn.

Arguments

xfloat, optional

Position on horizontal axis. The default is 0.

yfloat, optional

Position on vertical axis. The default is O.

namestr, optional

Friendly name for human readability. The default is None.

joint0Union[Joint, tuple[float]], optional

Linked pivot joint 1 (geometric constraints). The default is None.

joint1Union[Joint, tuple[float]], optional

Other pivot joint linked. The default is None.

distance0float, optional

Distance from joint0 to the current Joint. The default is None.

distance1float, optional

Distance from joint1 to the current Joint. The default is None.

_abc_impl = <_abc._abc_data object>
circle(joint)

Return the first link between self and parent as a circle.

Parameters:

joint (Joint) – Parent joint

Returns:

Circle is a tuple (abscisse, ordinate, radius).

Return type:

tuple[float, float, float]

get_constraints()

Return the two constraining distances of this joint.

r0
r1
reload()

Compute the position of pivot joint, use the two linked joints.

set_anchor0(joint, distance=None)

Set the first anchor for this Joint.

Parameters:

  • joint (Joint | tuple[float]) – The joint to use as anchor.

  • distance (float) – Distance to keep constant from the anchor. The default is None.

set_anchor1(joint, distance=None)

Set the second anchor for this Joint.

Parameters:

  • joint (Joint | tuple[float]) – The joint to use as anchor.

  • distance (float) – Distance to keep constant from the anchor. The default is None.

set_constraints(distance0=None, distance1=None)

Set geometric constraints.

Parameters:

  • distance0 – (Default value = None)

  • distance1 – (Default value = None)

class pylinkage.interface.joint.Static(x=0, y=0, name=None)

Bases: Joint

Special case of Joint that should not move.

Mostly used for the frame.

__init__(x=0, y=0, name=None)

A Static joint is a point in space to use as anchor by other joints.

It is NOT a kind of joint as viewed in engineering terms!

xfloat, optional

Position on horizontal axis. The default is 0.

yfloat, optional

Position on vertical axis. The default is O.

namestr, optional

Friendly name for human readability. The default is None.

_abc_impl = <_abc._abc_data object>
get_constraints()

Return an empty tuple.

reload()

Do nothing, for consistency only.

set_anchor0(joint)

First joint anchor.

Parameters:

joint –

set_anchor1(joint)

Second joint anchor.

Parameters:

joint –

set_constraints(*args)

Do nothing, for consistency only.

Parameters:

args – Unused

Linkage definition

The linkage module defines useful classes for linkage definition.

Created on Fri Apr 16, 16:39:21 2021.

@author: HugoFara

class pylinkage.interface.linkage.Linkage(joints, order=None, name=None)

Bases: object

A linkage is a set of Joint objects.

It is defined as a kinematic linkage. Coordinates are given relative to its own base.

__init__(joints, order=None, name=None)

Define a linkage, a set of joints.

Parameters:

  • joints (Iterable[Joint]) – All Joint to be part of the linkage.

  • order (Iterable[Joint]) – Sequence to manually define resolution order for each step. It should be a subset of joints. Automatic computed order is experimental! (Default value = None).

  • name (str) – Human-readable name for the Linkage. If None, take the value str(id(self)). (Default value = None).

_cranks
_solve_order
get_coords()

Return the positions of each element in the system.

get_num_constraints(flat=True)

Numeric constraints of this linkage.

Parameters:

flat (bool) – Whether to force one-dimensional representation of constraints. The default is True.

Returns:

List of geometric constraints.

Return type:

list

get_rotation_period()

The number of iterations to finish in the previous state.

Formally, it is the common denominator of all crank periods.

Returns:

Number of iterations with dt=1.

Return type:

int

hyperstaticity()

Return the hyperstaticity (over-constrainment) degree of the linkage in 2D.

joints
name
rebuild(pos=None)

Redefine linkage joints and given initial positions to joints.

Parameters:

pos (tuple[tuple[int]]) – Initial positions for each joint in self.joints. Coordinates do not need to be precise, they will allow us the best fitting position between all possible positions satisfying constraints. (Default value = None)

set_completely(dimensions, positions, flat=True)

Set both dimension and initial positions.

Parameters:

  • dimensions (tuple[float] | tuple[tuple[float, float]]) – List of dimensions.

  • positions (tuple[tuple[float, float]]) – Initial positions

  • flat (bool) – If the dimensions are in “flat mode”. The default is True.

set_coords(coords)

Set coordinates for all joints of the linkage.

Parameters:

coords –

set_num_constraints(constraints, flat=True)

Set numeric constraints for this linkage.

Numeric constraints are distances or angles between joints.

Parameters:

  • constraints (Iterable) – Sequence of constraints to pass to the joints.

  • flat (bool) – If True, constraints should be a one-dimensional sequence of floats. If False, constraints should be a sequence of tuples of digits. Each element will be passed to the set_constraints method of each corresponding Joint. (Default value = True)

step(iterations=None, dt=1)

Make a step of the linkage.

Parameters:

  • iterations (int) – Number of iterations to run across. If None, the default is self.get_rotation_period(). (Default value = None)

  • dt (float) – Amount of rotation to turn the cranks by. All cranks rotate by their self.angle * dt. The default is 1. (Default value = 1)

Returns:

Iterable of the joints’ coordinates.

Return type:

Generator[tuple[float, float]]

Exceptions

The exceptions module is a simple quick way to access the built-in exceptions.

Created on Wed Jun 16, 15:20:06 2021.

@author: HugoFara

exception pylinkage.interface.exceptions.HypostaticError(linkage, message='The system is hypo-static!')

Bases: Exception

The system is under-constrained and multiple solutions may exist.

__init__(linkage, message='The system is hypo-static!')
exception pylinkage.interface.exceptions.UnbuildableError(joint, message='Unable to solve constraints')

Bases: Exception

Should be raised when the constraints cannot be solved.

__init__(joint, message='Unable to solve constraints')