## Leg Actuators Specifications

| Actuator | Cont. force | Max force | Max speed | Nom. power | Max power |
|---|---|---|---|---|---|
| Hip Yaw | 630 N | 2 kN | 0.4 m/s | 230 W | 440 W |
| Hip Act 1 (Roll/Pitch) | 630 N | 2 kN | 0.4 m/s | 230 W | 440 W |
| Hip Act 2 (Roll/Pitch) | 630 N | 2 kN | 0.4 m/s | 230 W | 440 W |
| Leg Length | 1500 N | 5 kN | 0.625 m/s | 900 W | 2000 W |
| Ankle Act 1 | 630 N | 2 kN | 0.4 m/s | 230 W | 440 W |
| Ankle Act 2 | 630 N | 2 kN | 0.4 m/s | 230 W | 440 W |


The actuators have all the following sensors:
- motor side absolute position encoders
- current sensing for the motor phases
- temperature sensor for power electronics and motor stator
- absolute position encoders on the joint or the links 
- 1 DoF  load cell sensor at actuator output to measure actuator output force (leg joints) 
- Safe Torque Off safety signal 
- Current sensing on the input power bus to estimate power consumption of motro driver board

# Actuators and closed kinematic chains

Each leg of Kangaroo is a hybrid serial-parallel kinematic chain formed by four closed sub-mechanisms. All linear actuators are placed near the pelvis area, with motion transmitted to the joints through serial-parallel hybrid linkages. This design concentrates mass near the trunk, reducing leg inertia and improving impact resilience.

The sub-mechanisms and their kinematic complexity are summarised in the table below (from Mingo Hoffman et al., *Modeling and Numerical Analysis of Kangaroo Lower Body*, RAS 2026):

| Sub-mechanism | Type | Active DOFs | Passive DOFs | Constraints |
|---|---|---|---|---|
| Hip Yaw | 1DOF RRPR | 1 | 2 (3) | 2 |
| Hip Pitch/Roll | 2DOFs U-2RRPU | 2 | 8 (10) | 8 |
| Knee | 1DOF RRRR-RRRP-R | 1 | 6 (8) | 6 |
| Ankle Pitch/Roll | 2DOFs U-2(RRRP-RRR-UU) | 2 | 16 (24) | 16 |

```{figure} ../../_static/images/hip_yaw_pitch_roll-1.png
:name: hip-actuators
Hip yaw (1 active DoF) and hip pitch/roll (2 active DoF) actuators and joints layout.
```
```{figure} ../../_static/images/leg_length_ankle-1.png
:name: leglength-ankle-actuators
Leg length (1 active DoF) and ankle pitch/roll (2 active DoF) actuators and joints layout.
```

## 1DoF Hip Yaw

The Hip Yaw is a closed sub-mechanism modelled as a 1DOF RRPR linkage. It introduces 2 linear constraints and presents two kinematic singularities when the passive DOF θ is at 0 rad and −π rad — corresponding to the linear actuator being driven to approximately 0.05 m and −0.05 m respectively. These singular configurations lie outside the physical actuator stroke of (−0.011, 0.026) m, so they are never reached in practice.

**Joint limits:** −15° to +45° (actuator stroke −0.011 m to +0.026 m)

## 2DoFs Hip Pitch/Roll

The Hip Pitch/Roll sub-mechanism is a hybrid serial-parallel system equivalent to a U-2RRPU differential mechanism driven by two linear actuators in a differential configuration. It introduces 8 constraints and produces convex non-linear joint limits. A kinematic singularity arises when the two actuators are driven to their extremes differentially (approximately −0.04 m and +0.04 m), causing the Hip Roll passive DOF to approach ±π/2 rad. A mechanical limit on Hip Roll prevents reaching this configuration.

**Joint limits:** Hip Roll −25° to +25°; Hip Pitch −40° to +42°  (actuator stroke −0.04 m to +0.04 m)

## 1DoF Knee (Leg length)

The Knee is formed by three closed planar linkages (RRRR-RRRP-R) connecting the tibia to the hip. It is the only sub-mechanism with an absolute linear encoder mounted directly on its actuator, so no initial calibration procedure is needed. The Knee exhibits two primary singularities at 0 rad and −π rad of its passive DOF, corresponding to actuator positions of approximately +0.095 m and −0.095 m. The actuator stroke is limited to (−0.075, 0.075) m and additional hard plastic pads mechanically restrict the passive knee motion, preventing any singular configuration even in the event of a fall.

**Joint limits:** 0° to 120° (actuator stroke 0 m to 0.15 m)

## 2DoFs Ankle Pitch/Roll

The Ankle is the most complex sub-mechanism: a hybrid serial-parallel system composed of three sub-linkages (U-2(RRRP-RRR-UU)) that together introduce 16 constraints. The ankle actuators are located at the back of the femur and transmit motion to the foot via four-bar linkages, keeping all electronics and actuators above the knee for maximum impact resilience. Two absolute rotary encoders on the ankle are used for initial calibration of the passive DOFs.

The Ankle and Knee together form a non-linear transmission: when the Leg Length actuator retracts or extends, the Ankle Pitch passively compensates to keep the foot sole parallel to the ground, without requiring any Ankle actuator motion. Active Ankle actuation is only needed to override this passive compensation (e.g. to tilt the foot intentionally).

**Joint limits:** Ankle Roll −25° to +25°; Ankle Pitch −42.5° to +42.5° (actuator stroke −0.024 m to +0.024 m)