Simple axis pad

import matplotlib.pyplot as plt
import numpy as np

from matplotlib.projections import PolarAxes
from matplotlib.transforms import Affine2D
import mpl_toolkits.axisartist as axisartist
from mpl_toolkits.axisartist import angle_helper, grid_finder
from mpl_toolkits.axisartist.grid_helper_curvelinear import GridHelperCurveLinear


def setup_axes(fig, rect):
    """Polar projection, but in a rectangular box."""
    # see demo_curvelinear_grid.py for details
    grid_helper = GridHelperCurveLinear(
        Affine2D().scale(np.pi/180., 1.) + PolarAxes.PolarTransform(),
        extreme_finder=angle_helper.ExtremeFinderCycle(
            20, 20,
            lon_cycle=360, lat_cycle=None,
            lon_minmax=None, lat_minmax=(0, np.inf),
        ),
        grid_locator1=angle_helper.LocatorDMS(12),
        grid_locator2=grid_finder.MaxNLocator(5),
        tick_formatter1=angle_helper.FormatterDMS(),
    )
    ax = fig.add_subplot(
        rect, axes_class=axisartist.Axes, grid_helper=grid_helper,
        aspect=1, xlim=(-5, 12), ylim=(-5, 10))
    ax.axis[:].set_visible(False)
    return ax


def add_floating_axis1(ax1):
    ax1.axis["lat"] = axis = ax1.new_floating_axis(0, 30)
    axis.label.set_text(r"$\theta = 30^{\circ}$")
    axis.label.set_visible(True)

    return axis


def add_floating_axis2(ax1):
    ax1.axis["lon"] = axis = ax1.new_floating_axis(1, 6)
    axis.label.set_text(r"$r = 6$")
    axis.label.set_visible(True)

    return axis


fig = plt.figure(figsize=(9, 3.))
fig.subplots_adjust(left=0.01, right=0.99, bottom=0.01, top=0.99,
                    wspace=0.01, hspace=0.01)


def ann(ax1, d):
    ax1.annotate(d, (0.5, 1), (5, -5),
                 xycoords="axes fraction", textcoords="offset points",
                 va="top", ha="center")


ax1 = setup_axes(fig, rect=231)
axis = add_floating_axis1(ax1)
ann(ax1, "default")

ax1 = setup_axes(fig, rect=232)
axis = add_floating_axis1(ax1)
axis.major_ticklabels.set_pad(10)
ann(ax1, "ticklabels.set_pad(10)")

ax1 = setup_axes(fig, rect=233)
axis = add_floating_axis1(ax1)
axis.label.set_pad(20)
ann(ax1, "label.set_pad(20)")

ax1 = setup_axes(fig, rect=234)
axis = add_floating_axis1(ax1)
axis.major_ticks.set_tick_direction("in")
ann(ax1, 'ticks.set_tick_direction("in")')

ax1 = setup_axes(fig, rect=235)
axis = add_floating_axis1(ax1)
axis.major_ticks.set_tick_direction("out")
ann(ax1, 'ticks.set_tick_direction("out")')

ax1 = setup_axes(fig, rect=236)
axis = add_floating_axis1(ax1)
axis.major_ticks.set_tick_direction("inout")
ann(ax1, 'ticks.set_tick_direction("inout")')

plt.show()