Design of a novel sidemounted leg mechanism with high flexibility for a multimission quadruped earth rover BJTUBOT
Yifan WU, Sheng GUO, Luquan LI, Lianzheng NIU, Xiao LI
Design of a novel sidemounted leg mechanism with high flexibility for a multimission quadruped earth rover BJTUBOT
Earth rover is a class of emerging wheeledleg robots for nature exploration. At present, few methods for these robots’ leg design utilize a sidemounted spatial parallel mechanism. Thus, this paper presents a complete design process of a novel 5degreeoffreedom (5DOF) hybrid leg mechanism for our quadruped earth rover BJTUBOT. First, a general approach is proposed for constructing the novel leg mechanism. Subsequently, by evaluating the basic locomotion task (LT) of the rover based on screw theory, we determine the desired motion characteristic of the sidemounted leg and carry out its two feasible configurations. With regard to the synthesis method of the parallel mechanism, a family of concise hybrid leg mechanisms using the 6DOF limbs and an L_{1F1C} limb (which can provide a constraint force and a couple) is designed. In verifying the motion characteristics of this kind of leg, we select a typical (3UPRU&RRRR)&R mechanism and then analyze its kinematic model, singularities, velocity mapping, workspace, dexterity, statics, and kinetostatic performance. Furthermore, the virtual quadruped rover equipped with this innovative leg mechanism is built. Various basic and specific LTs of the rover are demonstrated by simulation, which indicates that the flexibility of the legs can help the rover achieve multitasking.
design synthesis / parallel mechanism / hybrid leg mechanism / screw theory / quadruped robot
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Abbreviations  
C  Cylindrical joint 
COM  Center of mass 
DOF  Degreeoffreedom 
GCI  Global conditioning index 
L_{1F1C}  Passive constraining limb provides both a constraint force and a constraint couple 
LCI  Local condition index 
LT  Locomotion task 
MF  Motion form 
P  Prismatic joint 
P  Prismatic joint with actuation 
R  Revolute 
R  Revolute joint with actuation 
R_{1}  Type1 revolute joint 
R_{2}  Type2 revolute joint 
S  Spherical joint 
T  Translation 
U  Universal joint 
Variables  
a_{i}  Vector $\rightharpoonup {O}_{\mathrm{B}}{A}_{i}$ 
${}^{}\mathrm{B}{\mathit{a}}_{i}$  a_{i} in the base coordinate 
$\Vert \mathit{A}\Vert $  Frobenius norm of matrix A_{m×n} 
b_{i}  Vector $\rightharpoonup {O}_{\mathrm{P}}{B}_{i}$ 
${}^{}\mathrm{B}{\mathit{b}}_{i}$  b_{i} in the base coordinate 
d  Dimension of the wrench system 
d  Vector $\rightharpoonup CD$ 
d'  Vector $\rightharpoonup {O}_{B}{D}^{\mathrm{\prime}}$ 
e  Vector $\rightharpoonup DE$ 
e'  Vector $\rightharpoonup {O}_{\mathrm{B}}{E}^{\mathrm{\prime}}$ 
f  Constraint force 
F  A support force or static friction 
F_{1}  Support force along the yaxis 
F_{2}, F_{3}  Static frictions along the x and zaxis, respectively 
F_{1}(t), F_{2}(t), F_{3}(t)  Timevarying functions of F_{1}, F_{2}, and F_{3}, respectively 
G  Gravity force 
h  Height of the sidemounted base along the yaxis 
J  Jacobian matrix of the 3UPRU&RRRR parallel mechanism 
J_{c_RRRR}  Constraint Jacobian for the RRRR limbs 
J_{k_UPRU}  Actuation Jacobian for the UPRU limbs 
${\mathit{J}}_{v}$  Linear velocity mapping part of J 
${\mathit{J}}_{\omega}$  Angular velocity mapping part of J 
k  Vector $\rightharpoonup {O}_{\mathrm{P}}K$ 
${}^{}\mathrm{B}\mathit{k}$  k in the base coordinate 
${}^{}\mathrm{P}\mathit{k}$  k in the moving platform coordinate 
${}^{}\mathrm{W}\mathit{k}$  k in the wheel coordinate 
$k\left(\mathit{J}\right)$  Condition number of the Jacobian matrix J 
l_{i}  Length of the vector $\rightharpoonup {A}_{i}{B}_{i}$ 
${\mathit{l}}_{i}$  Vector $\rightharpoonup {A}_{i}{B}_{i}$ 
${\dot{l}}_{i}$  Linear velocity of the P joint 
l_{max}  Maximum length of the P joint 
l_{min}  Minimum length of the P joint 
$\dot{\mathit{L}}$  Vector which contains all velocities of the P joints 
m  Constraint couple 
M  Torque caused by friction 
$M\left(t\right)$  Timevarying function of M 
N  Support force 
O_{B}  Original point of the base coordinate system 
O_{P}  Original point of the moving platform coordinate system 
O_{W}  Original point of the legend coordinate system 
p  Vector $\rightharpoonup {O}_{\mathrm{B}}{O}_{\mathrm{P}}$ 
p_{W}  Vector $\rightharpoonup {O}_{\mathrm{B}}{O}_{\mathrm{W}}$ 
${}^{}\mathrm{B}{\mathit{p}}_{\mathrm{W}}$  Position vector of the legend in the base coordinate 
${\dot{q}}_{ij}$  Intensity of the jth joint in the ith limb 
$\dot{\mathit{Q}}$  Velocity vector of all joints 
r  Location vector of the twist $ 
r_{i}  Location vector of the ith twist or screw $_{i} 
${\mathit{r}}_{d}^{\mathrm{r}}$  Location vector of the dth constraint screw ${S\phantom{\rule{0.583em}{0ex}}/}_{d}^{\mathrm{r}}$ 
${}^{}\mathrm{B}{\mathit{R}}_{\mathrm{P}}$  Rotation matrix from the moving platform frame to the base frame 
${}^{}\mathrm{B}{\mathit{R}}_{\mathrm{W}}$  Rotation matrix from the legend frame to the base frame 
${}^{}\mathrm{P}{\mathit{R}}_{\mathrm{W}}$  Rotation matrix from the legend frame to the moving platform frame 
${}^{}\mathrm{W}{\mathit{R}}_{\mathrm{P}}$  Inverse of ${}^{}\mathrm{P}{\mathit{R}}_{\mathrm{W}}$ 
s  Direction vector of the twist $ 
s_{i}  Direction vector of the ith twist or screw $_{i} 
${\mathit{s}}_{ij}$  Direction vector of ${S\phantom{\rule{0.583em}{0ex}}/}_{ij}$ 
${\mathit{s}}_{d}^{\mathrm{r}}$  Direction vector of the dth constraint screw ${S\phantom{\rule{0.583em}{0ex}}/}_{d}^{\mathrm{r}}$ 
t  Time 
u_{li}  Unit vector of P joint 
u_{d}  Unit vector of the linkage CD 
${}^{}\mathrm{B}{\mathit{u}}_{li}$  u_{li }in the base coordinate 
${}^{}\mathrm{B}\mathit{v}$  Vector v in the base frame 
${}^{}\mathrm{B}{\mathit{v}}_{{O}_{\mathrm{P}}}$  Linear velocity of moving platform 
${}^{}\mathrm{P}\mathit{v}$  Vector v in the moving platform frame 
${}^{}\mathrm{W}\mathit{v}$  Vector v in the legend frame 
w  Width of the sidemounted base along the xaxis 
w  Vector $\rightharpoonup K{O}_{\mathrm{W}}$ 
WS  Workspcae 
x  xaxis of the base coordinate system 
$\dot{x}$  Velocity in the x direction 
x_{P}  xaxis of the moving platform coordinate system 
$x\left(t\right)$  Position function on the xaxis 
$\dot{\mathit{X}}$  Velocity of moving platform 
y  yaxis of the base coordinate system 
$\dot{y}$  Velocity in the y direction 
y_{P}  yaxis of the moving platform coordinate system 
$y\left(t\right)$  Position function on the yaxis 
z  zaxis of the base coordinate system 
z_{P}  zaxis of the moving platform coordinate system 
α  Attitude angle about the xaxis 
$\dot{\alpha}$  Velocity of α 
${\alpha}^{\prime}$  Rotation angle about the x_{P}axis 
${\alpha}^{\prime}\left(t\right)$  Orientation function about α' 
β  Attitude angle about the yaxis 
$\dot{\beta}$  Velocity of β 
γ  Attitude angle about the zaxis 
$\dot{\gamma}$  Velocity of γ 
γ'  Rotation angle about the z_{P}axis 
${\gamma}^{\prime}\left(t\right)$  Orientation function about γ' 
${\eta}_{i}$  Value of GCI 
${\eta}_{v}$, ${\eta}_{\omega}$  GCI of the linear and angular motions, respectively 
θ  Rotation angle of the R joint in the RRRR limb 
$\dot{\theta}$  Angular velocity of active R joint 
${\dot{\theta}}_{in}$  Intensity or angular velocity of the passive joints 
φ  Rotation angle of the steering R joint connected with the legend 
${}^{}\mathrm{B}\text{\omega}$  Angular velocity of moving platform 
$\delta \dot{\mathit{Q}}$  Driving velocity deviation 
$  A screw or a twist 
$^{r}  A wrench system 
$_{i}  ith twist or screw 
${S\phantom{\rule{0.583em}{0ex}}/}_{ij}$  Unit screw of the jth joint in the ith limb 
${S\phantom{\rule{0.583em}{0ex}}/}_{\mathrm{P}}$  Instantaneous twist of the moving platform 
${S\phantom{\rule{0.583em}{0ex}}/}_{d}^{\mathrm{r}}$  dth constraint screw 
${S\phantom{\rule{0.583em}{0ex}}/}_{i}^{\mathrm{r}}$  Reciprocal screws for the ith UPRU limb 
$\delta {S\phantom{\rule{0.583em}{0ex}}/}_{\mathrm{P}}$  Velocity deviation of the moving platfrom 
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